Chapter 1
Basic diode laser
engineering principles
Main Chapter Topics
1.1
1.2
1.3
Brief recapitulation
1.1.1 Key features of a diode laser
1.1.2 Homojunction diode laser
1.1.3 Double-heterostructure diode laser
1.1.4 Quantum well diode laser
1.1.5 Common compounds for semiconductor lasers
Optical output power – diverse aspects
1.2.1 Approaches to high-power diode lasers
1.2.2 High optical power considerations
1.2.3 Power limitations
1.2.4 High power versus reliability tradeoffs
1.2.5 Typical and record-high cw optical output powers
Selected relevant basic diode laser characteristics
1.3.1 Threshold gain
1.3.2 Material gain spectra
1.3.3 Optical confinement
1.3.4 Threshold current
1.3.5 Transverse vertical and transverse lateral modes
1.3.6 Fabry–Pérot longitudinal modes
1.3.7 Operating characteristics
1.3.8 Mirror reflectivity modifications
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Semiconductor Laser Engineering, Reliability and Diagnostics: A Practical Approach to High Power
and Single Mode Devices, First Edition. Peter W. Epperlein.
C 2013 John Wiley & Sons, Ltd. Published 2013 by John Wiley & Sons, Ltd.
4
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
1.4
Laser fabrication technology
1.4.1 Laser wafer growth
1.4.2 Laser wafer processing
1.4.3 Laser packaging
References
81
82
84
86
96
Introduction
This chapter starts with a brief recap of the fundamental aspects and elements of diode
lasers, including relevant features of the standard device types, with an emphasis on
the advantages of quantum heterostructures for their effective use as active regions
in the lasers. Common laser material systems are then discussed, along with lasing
wavelength-dependent applications and best output power levels achieved in each
individual high-power diode laser category for illustration and comparison. Various
aspects of high-power issues are presented, including power-limiting factors and
reliability tradeoffs. To develop a good understanding of diode laser operation, key
electrical, optical and thermal parameters and characteristics are described. The
chapter concludes with a description of the basic aspects of diode laser fabrication
and packaging technologies.
1.1
1.1.1
Brief recapitulation
Key features of a diode laser
The basic device structure consists of a rectangular parallelepiped of a direct bandgap
semiconductor, usually a III–V compound semiconductor such as GaAs, incorporating a forward-biased, heavily doped p–n junction to provide the optical gain medium
in a resonant optical cavity, as illustrated schematically in Figure 1.1.
Further basic elements include the optical confinement in the transverse vertical
direction perpendicular to the active region and transverse lateral confinement of
injected current, carriers and photons parallel to the active layer. Further details of
these features will be illustrated below.
1.1.1.1
Carrier population inversion
The operating principle of a semiconductor laser requires the gain medium to be
pumped with some external energy source, either electrical or optical, to build up
and maintain a nonequilibrium distribution of charge carriers, which has to be large
enough to enable a population inversion for the generation of optical gain. Pumping
realized by optical excitation of electron–hole pairs is usually only important for the
rapid characterization of the quality of the laser material without electrical contacts.
The more technologically important technique, however, is direct electrical pumping
using a forward-biased semiconductor diode with a heavily doped p–n junction at the
center of all state-of-the-art semiconductor injection lasers, that is, diode lasers. The
BASIC DIODE LASER ENGINEERING PRINCIPLES
5
Figure 1.1 Illustration of a very basic diode laser chip. Typical dimensions in x direction
are approximately 500 μm for the laser cavity length, in y direction 100 μm for the transverse
lateral coordinate without lateral confinement structure, and in z direction a few micrometers
for the transverse vertical extent of the p–n layer stack only (substrate not shown). The active
layer structure depends on the transverse vertical layer configuration, which will be discussed
along with different lateral confinement structures in some of the sections further below.
Fermi levels in these heavily doped and therefore degenerate n- and p-type materials
lie in the conduction and valence band, respectively. With no bias voltage applied,
the quasi-Fermi levels are identical across the p–n junction at thermal equilibrium
with the conduction and valence bands bent, as shown in Figure 1.2a. In this steady
state, further diffusion of electrons and holes across the p–n boundary is opposed by
the built-in potential (diffusion potential) resulting from the depletion layer or spacecharge region formed by the negatively charged acceptors and positively charged
donors on the p- and n-sides, respectively. Simplified expressions for the depletion
layer width W and built-in potential Vbi can be written as follows:
2ε
W =
q
Vbi =
Na + Nd
Na Nd
Nd Na
kB T
ln
q
n i2
1/2
Vbi
(1.1)
(1.2)
where ε = εr ε0 is the permittivity, q is the electron charge, T is the absolute temperature, kB is the Boltzmann constant, Na and Nd are the densities of acceptors and
donors, respectively, and n i2 = np is the square of the intrinsic carrier concentration,
with n the electron density in the conduction band and p the hole density in the valence
band, and with all shallow donors and acceptors fully ionized at room temperature
(Sze, 1981).
When the p–n junction is forward biased by applying an external voltage nearly
equal to the energy bandgap voltage, the built-in electric field is reduced, and
6
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.2 Energy band diagram of a heavily doped p–n junction at (a) zero bias and
(b) forward bias. Dashed lines represent the quasi-Fermi levels. Schematic representation of
densities and strong injections of electrons (e) and holes (h) under forward bias close to the
energy gap voltage causing population inversion and radiative recombinations of electrons and
holes in the narrow depletion zone.
free electrons and holes can diffuse across the junction into the p- and n-regions,
respectively.
Figure 1.2b shows that electrons are then injected into the conduction band and
holes into the valence band and for sufficient numbers can create a population inversion in a very narrow zone. In this so-called active region, electrons and holes
can recombine, and photons, generated in the radiative recombination process with
energies of about the bandgap energy Eg , can be reabsorbed or can induce stimulated emission. The following section treats the optical processes responsible for the
generation of optical gain. Issues linked to the simple p–n junction approach and
more efficient p–n junction configurations will be discussed in those sections dealing
with different diode laser structures.
1.1.1.2
Net gain mechanism
Figure 1.3 shows a simplified illustration of different electronic transitions between
the conduction and valence bands, which are important for establishing an optical
gain mechanism. There are three basic types of radiative band-to-band transitions: (i)
spontaneous emission; (ii) photon absorption, also called stimulated absorption; and
(iii) stimulated emission.
BASIC DIODE LASER ENGINEERING PRINCIPLES
7
Figure 1.3 Energy level diagram illustrating electronic transitions between the conduction
and valence bands of a nonequilibrium, degenerate, direct semiconductor at different rates R:
Rspon represents the spontaneous emission with an electron (occupied state, solid circles) in
the conduction band recombining with a hole (unoccupied state, open circles) in the valence
band. Rabs depicts the photon absorption process from an occupied state in the valence band
to an unoccupied state in the conduction band by generating an electron–hole pair leaving an
electron in the conduction band and a hole in the valence band. The required incident photon
energy has to be ≥EFc − EFv where EFv is negative with the zero-point of energy at the top edge
of the valence band. Rstim shows the stimulated emission process where an incident photon
with sufficient energy stimulates the recombination of a conduction band electron with a hole
in the valence band by producing a second photon, which has the same phase, wavelength,
and direction of propagation as the incoming photon. This photon multiplication process is the
basis for generating optical gain and coherent emission.
Most transitions of interest involve electrons and holes close to the bottom of
the conduction band and to the top of the valence band, respectively, because carrier
densities are highest there. Assuming the energy of an electron is E2 , and of a hole
E1 , then the energy of a photon emitted in a recombination process is E21 = hν ∼ Eg ,
which can be slightly higher than the bandgap energy; here h is the Planck constant
and ν the photon frequency.
In the spontaneous emission process, the radiative recombination of an electron–
hole pair generates a photon. This process is random in direction, time and phase,
but does not lead to a coherent radiation when averaged over a large ensemble of
emission processes. The spontaneous emission does not interact with photons through
the recombination process, in contrast to the absorption and stimulated emission
processes, which will be discussed next. Therefore, the transition rate for spontaneous
emission, Rspon , is not dependent on the photon density, but is proportional to the
product of the electron concentration at E2 and hole concentration at E1 . The former
is the product of the density of electronic states Dc (E2 − Ec ) and the probability that
these states are occupied by electrons given by the Fermi–Dirac distribution function
f2 , whereas the latter is the product of the density of states Dv (Ev − E1 ) and the
8
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
probability (1 − f1 ) that these states are not occupied by electrons. Ec and Ev are the
energies at the conduction band minimum and valence band maximum, respectively.
Thus, we can write
Rspon = A21 Dc (E 2 − E c ) f 2 Dv (E v − E 1 ) (1 − f 1 ) .
(1.3)
Here A21 is the transition probability for spontaneous emission from the energy state
E2 to E1 .
In the absorption process, a photon with energy E2 − E1 ≥ Eg is absorbed and
excites an electron in the conduction band while leaving a hole in the valence band.
Therefore, absorption is a three-particle process and its transition rate Rabs from E1 to
E2 is proportional to the product of three particle concentrations: the photon density
nphot (E2 − E1 ); the density of unoccupied states Dc (E2 − Ec )(1 – f2 ) in the conduction
band; and the density of occupied states Dv (Ev − E1 )f1 in the valence band. With B12 ,
the transition probability constant, we obtain
Rabs = B12 n phot (E 2 − E 1 ) Dv (E v − E 1 ) f 1 Dc (E 2 − E c ) (1 − f 2 ) .
(1.4)
In contrast to stimulated absorption discussed above, the various interactions
involved in the stimulated emission process are reversed, that is, an incident photon
stimulates the recombination of an electron–hole pair by simultaneously generating
the emission of a new photon. This is a positive gain mechanism leading to the
amplification of radiation, because the stimulated photons, which are aligned in
direction and phase to the incident photons, are emitted into the incident radiation
field resulting in a strong coherent optical emission. Of course, the effective net gain is
dependent on the difference between the transition rates of stimulated emission and
absorption. The rate of stimulated emission is proportional to the incident photon
density nphot (E2 − E1 ), the density of occupied states Dc (E2 − Ec )f2 in the conduction
band, and the density of unoccupied states Dv (Ev − E1 )(1 − f1 ) in the valence band.
It can be written as
Rstim = B21 n phot (E 2 − E 1 ) Dc (E 2 − E c ) f 2 Dv (E v − E 1 ) (1 − f 1 )
(1.5)
where B21 is the probability of the stimulated emission transition.
At thermal equilibrium of the semiconductor, there is no net energy transfer to
the optical field, that is, the transition rates for spontaneous emission, stimulated
emission, and absorption have to obey the following equation:
Rabs = Rstim + Rspon .
(1.6)
By using Equations (1.3) to (1.6), and the well-known expressions for the Fermi–
Dirac distribution function f and the black-body radiation according to Planck’s
theory, we obtain after some simple algebraic manipulations
A21 =
n r3
2
π 3 c 3
(E 2 − E 1 )2 B21
(1.7)
BASIC DIODE LASER ENGINEERING PRINCIPLES
9
and
B21 = B12
(1.8)
where nr is the refractive index of the medium, c is the velocity of light in vacuum,
= h/2π , and (E2 − E1 ) = hν is the photon energy. Equations (1.7) and (1.8) are the
Einstein relations for radiative transitions.
In the following, we derive the necessary condition for net gain under nonequilibrium conditions, that is, strong carrier injections, by calculating the ratio between
the transition rates for absorption and stimulated emission. We use Equation (1.4) for
Rabs and (1.5) for Rstim , and the well-known expressions for the separate quasi-Fermi
functions f1 and f2 in the valence and conduction bands, respectively. We obtain
Rabs
f 1 (1 − f 2 )
exp{(E 2 − E Fc )/k B T }
= exp{[hν − (E Fc − E Fv )]/k B T }
=
=
Rstim
f 2 (1 − f 1 )
exp{(E 1 − E Fv )/k B T }
(1.9)
with the quasi-Fermi level energies EFc for the conduction band and EFv for the
valence band. The exponential function is greater than one for EFc = EFv at thermal
equilibrium and hence Rabs > Rstim always. However, Equation (1.9) clearly shows
that lasing operation can be achieved for the condition
(E Fc − E Fv ) > hν > E g
(1.10)
involving photons with energies larger than the bandgap energy. A semiconductor
meeting the condition in Equation (1.10) is in the state of population inversion resulting in Rstim > Rabs , or, in other words, a photon is amplified rather than absorbed.
Equation (1.10) establishes the gain bandwidth of the medium including the requirement (EFc – EFv ) > Eg for having gain at any frequency. The limiting case
E Fc − E Fv = E g
(1.11)
is called the transparency condition, where the gain is zero for a photon frequency
ν = Eg /h. When the density of injected carriers is larger than the transparency density,
then (EFc − EFv ) > Eg and a net gain develops for photon energies between Eg and
(EFc – EFv ) according to Equation (1.10). We will resume the discussion of gainrelated issues in Section 1.3.
1.1.1.3
Optical resonator
To provide positive feedback for laser action, edge-emitting diode lasers usually
employ a Fabry–Pérot resonator comprising two parallel, high-quality plane mirrors
as shown in Figure 1.4. In semiconductors, this is easily achieved by cleaving the
crystal perpendicular to the cavity at the end faces along well-defined crystal planes.
For GaAs the cleaved facets are (110) planes and the junction plane comprising the
active layer is (100). Since the refractive index of the medium is very large (e.g., 3.6
10
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.4 Schematics of a semiconductor diode laser illustrating the formation of a standing
wave or longitudinal mode inside the gain medium of a Fabry–Pérot optical cavity with cleaved,
uncoated facets at the end faces, which act as partially reflecting mirrors. The mode propagates
in a dielectric waveguide with an effective refractive index determined by the indices of the
waveguide core and claddings. The laser is likely to oscillate at a frequency that matches a
longitudinal mode supported by the resonator.
for GaAs), the reflectivity of uncoated facet mirrors is already sufficiently high to
produce a resonant cavity and provide the feedback for the onset of laser oscillations.
Typical (power) reflectivities R of 32% for GaAs can be calculated from the Fresnel
reflection at normal incidence at the GaAs/air interface
R=
(n rs − n ra )2 + κ 2 ∼ (n rs − n ra )2
=
(n rs + n ra )2 + κ 2
(n rs + n ra )2
(1.12)
where nrs is the refractive index of the semiconductor, nra the index of the ambient air
in this case, and κ the extinction coefficient. For κ 2 (nrs – nra )2 , Equation (1.12)
simplifies and R depends only on the refractive indices.
To maximize laser functionality, mirrors are coated with appropriate dielectric
layers to adjust the reflectivities, which are usually very high (>90%) at the rear
mirror and lower (<10%) at the output front mirror of the laser cavity. Section 1.3
gives a detailed account of this topic.
The optical modes of this resonator can be considered as the superposition of two
plane light waves propagating normal to the mirror surfaces in opposite directions
along the resonator axis in a laser active material of length L and refractive index
nr,eff . A standing wave develops between the mirrors when the cavity length is an
integral number of half wavelengths
L=m
l0
l
=m
2
2n r,eff
(1.13)
where m is a positive integer and the number of nodes of the standing wave, l 0 is
the wavelength in vacuum. Equation (1.13) implies that the electric field is zero at
BASIC DIODE LASER ENGINEERING PRINCIPLES
11
both mirror surfaces. In Section 1.3, we will use the phase condition expressed in
Equation (1.13) to describe the development of longitudinal laser modes.
1.1.1.4
Transverse vertical confinement
In order to achieve high gain, the photon density in the active region, where the gaingenerating recombination processes are occurring, has to be maximized. This means
that the all-important stimulated emission has to dominate the spontaneous emission,
which can be evaluated from the transition rate ratio Rstim /Rspon . Using Equations
(1.5), (1.3) and (1.7), (1.8), we obtain
Rstim
π 2 3 c 3
= 3
n phot (hν) .
Rspon
n r (hν)2
(1.14)
Here we have again used hν = E2 − E1 for the photon energy. This equation clearly
demonstrates the dominance of the stimulated emission over the spontaneous emission, increasing with increasing density of photons nphot (hν) of energy hν. However,
it also shows that this photon density has to be much higher for lasers operating at
higher energies hν to compensate for the inverse squared photon energy dependence
in Equation (1.14).
In the previous section, we showed how to increase the photon density by optical
feedback in a resonator cavity. By bandgap engineering, effective structures perpendicular to the active layer have been developed to confine photons and charge carriers
in the laser active region. Such structures include double-heterostructures (DHs) and
quantum wells (QWs), schematically shown in Figure 1.5. Aspects of these structures
can be found in Sections 1.1.3, 1.1.4 and 1.3.
Electrons and holes are confined in the thin slab of undoped active material
sandwiched between n- and p-doped cladding layers and are then forced to recombine
E
Ec
Ec
n
P
Eg,cl
Eg,act
n
P
z
QW
Eg,SCH
Ev
Ev
(a)
(b)
Figure 1.5 Schematic illustration of two examples for vertical transverse confinement structures of an edge-emitting (in junction plane) diode laser: (a) double heterostructure and (b)
quantum well (QW) embedded in separate-confinement heterostructure (SCH). Simplified energy band diagrams (effects of band bending in the heterojunctions are ignored) versus vertical
direction z for a thin slab of undoped active material sandwiched between p- and n-doped
cladding layers.
12
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
inside this thin active layer. Typical thicknesses for DH and QW carrier-confining
active layers are about 0.1–0.2 μm and about 10 nm, respectively. The cladding layers
have a higher conduction–valence bandgap energy, which leads to a couple of positive
effects.
First, the three-layer structure acts like an optical waveguide in a vertical direction
since usually semiconductors with higher bandgap energy have a lower refractive
index than semiconductors with a low bandgap energy. Second, light generated in the
low-bandgap active layer will not be lost by reabsorption in the cladding layers.
The optical confinement in the transverse vertical direction is low because of the
thin active layers, and typical confinement factors can be as low as 20% and far below
1% for DH and QW structures, respectively, for refractive index differences between
cladding and active layers of about 5%. However, there are structures available for
improving the optical confinement in QW structures, and include surrounding the
active layer with a thicker separate-confinement heterostructure (SCH) region with
higher bandgap and lower refractive index to enhance the confinement of photons
(and electrons). The advantages of such structures will be discussed in Section 1.3
and the fundamental transverse vertical mode in Chapter 2.
1.1.1.5
Transverse lateral confinement
In transverse lateral confinement, not only are carriers and photons confined in a
direction parallel to the active layer, but so too is the current flowing through the
device in a vertical direction. This triple confinement scheme is designed to deliver
edge-emitting (in the plane of the active layer) diode lasers operating in fundamental
single-mode with high external efficiency and output power and at low threshold
current. These topics and parameters will be described in detail in Section 1.3 and
Chapter 2.
It is important to maximize the current injected into the active region by minimizing the leakage current, which is the difference between the total current injected
into the laser device and the current passing through the active region. The lower
the leakage current, the lower the probability that the output power saturates at high
currents. Also, under continuous wave (cw) operation of the laser there is then only
a small or negligible additional heating effect that can lead to a rollover of the light–
current characteristic, resulting in a decrease of optical output power with increasing
current (see Section 1.2.3.2). Current confinement can simply be realized by reducing the area of current injection just by limiting the contact area. However, the most
effective current confinement is combined with schemes to laterally confine carriers
and photons in the same configuration.
As discussed in the previous section, optical wave confinement in the vertical direction perpendicular to the active junction layer is formed by dielectric waveguiding.
This is also known as index-guiding because the refractive index of the active layer
is higher than that of the surrounding cladding layers, resulting in mode confinement
through total internal reflection at the active layer/cladding interfaces.
However, optical field confinement in the lateral direction can be grouped into
two classes, gain-guiding and index-guiding, dependent on whether the mode is
BASIC DIODE LASER ENGINEERING PRINCIPLES
p-contact
I.I.
p
n
I.I.
p
acve
layer
n
acve
layer
n-sub.
n-sub.
n-contact
(a)
p-contact
oxide
13
p
Ins.
Ins.
n
n-sub.
n-contact
(b)
(c)
Figure 1.6 Schematic cross-section of lateral confinement structures. (a) Proton stripe realized by ion implantation (I.I.) provides gain guiding; region implanted by protons is of high
resistivity restricting the current flow to an opening in the implanted region. (b) Simple rib
waveguide provides weak index-guiding. (c) Etched-mesa (ideal) buried-heterostructure sandwiched laterally between insulating (Ins.), highly resistive current blocking layers with higher
bandgap energies and lower refractive indices than those of the active layer provides strong
index-guiding. Alternatively, semi-insulating materials or reverse-biased p–n junctions formed
by regrowth can also be used as current blocking layers.
confined by the lateral variation of the optical gain or the refractive index, respectively.
Index-guided devices are further subdivided into weakly and strongly index-guided,
depending on the strength of the lateral index step.
Figure 1.6 shows schematically the three classes. Each class is represented by a
typical design selected from the numerous different approaches available to realize
the lateral confinement of current, carriers and photons. As will be shown in detail
in Section 1.3, gain-guiding provides current confinement, weak index-guiding current and photon confinement, and strong index-guiding provides current, carrier and
photon confinement.
1.1.2
Homojunction diode laser
As described in Sections 1.1.1.1 to 1.1.1.3, the key parts and processes of a homojunction laser include:
r direct electrical pumping by strong electron and hole injection of a forward-
biased (V ∼
= Eg /q) p–n junction with both p- and n-type regions of the same
material heavily doped to 1018 atoms/cm3 ;
r carrier recombination and population inversion in the narrow active region;
and
r optical feedback of the stimulated photons for coherent emission in an optical
resonator.
The first semiconductor lasers employed homojunctions and were plagued by
serious problems. One of the main constraints of this laser type results from the very
small potential barrier that an electron encounters when it is injected into the p-region
14
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
and from its high mobility μn . The penetration depth d of the electron is then given
by the diffusion length Ln
d = Ln =
Dn τn
(1.15)
where Dn is the diffusion coefficient and τ n is the lifetime of the electron established
by electron–hole recombination. Dn can be calculated from the mobility by using the
Einstein relation
Dn =
kB T
μn .
q
(1.16)
∼ 2 × 1018 cm−3 , the electron mobility is about 300 cm2 /
In GaAs, doped to n =
(V s) at room temperature (Yu and Cardona, 2001). This corresponds to a diffusion
coefficient of Dn ∼
= 8 cm2 /s. On the other hand, relevant mobility and diffusion
coefficient values for holes are lower by a factor of about 20, and hence have only a
negligible effect on the thickness of the effective recombination region. The electrons
injected into the p-region become minority carriers in a sea of holes with a density
of pp and their lifetimes can be approximated by
τn ≈
1
.
Bp p
(1.17)
With typical values for the bimolecular recombination coefficient of B ≈
2 × 10−10 cm3 /s, which is valid for most III–V compound semiconductors, and for
pp = 2 × 1018 cm−3 , the effective lifetime of an injected electron is τ n = 2.5 ns.
Using these values for Dn and τ n in GaAs we get a diffusion length Ln of about 1.5
μm. This shows that the active region is quite thick compared to the thickness of the
depletion layer of typically 0.1 μm. The region of inversion is located approximately
1.5 μm on the p-side of the junction. Since the diffusion length of the injected charge
carriers is controlled by recombination, there is little control over the extent of the
gain region. One of the problems with the homojunction laser is the poor overlap of
the small gain region with the spatial laser mode. However, a much bigger problem is
the very high threshold current density that usually requires the laser to be operated
pulsed at room temperature or cw at cryogenic temperatures. Actually, there are two
main reasons for the high threshold current.
The first reason can be evaluated from the current density necessary to generate
gain. To establish this carrier density in a depth d, regardless of the dimensions of
the diode laser, a current density of J = qdG is required, where d is the electron
penetration depth equal to the diffusion length Ln in a homojunction and G is the
necessary pumping rate to maintain a steady state population inversion. Under steady
state conditions, the injection rate must equal the recombination rate. G can be evaluated from G = Bnp and results in approximately 8 × 1026 electron–hole pairs/(cm3
s) to establish a carrier density of 2 × 1018 cm−3 for both electrons and holes usually
BASIC DIODE LASER ENGINEERING PRINCIPLES
15
Figure 1.7 Schematic illustration of the poor overlap between optical mode and gain region,
and the high absorption losses of the laser beam in a homojunction device.
required to form a population inversion, and by using for the bimolecular recombination coefficient B ≈ 2 × 10−10 cm3 /s and for the diffusion length Ln = d = 1.5 μm.
Finally, we get J ∼
= 19 × 103 A/cm2 for the first contribution to the threshold current
density.
The second reason lies in the fact that, due to the large transverse dimensions,
the laser beam extends considerably into the n- and p-regions where it is strongly absorbed; in other words, the region outside the inversion introduces a strong absorption
loss (Figure 1.7).
As will be discussed in Section 1.3, gain exists only for light with energy slightly
greater than the bandgap energy. Moreover, there is no mode confinement or waveguiding of the laser mode having a size of some micrometers, with the consequence that
the beam will spread to larger sizes in a short distance due to strong diffraction effects
leading to even larger absorption losses and a smaller overlap with the gain region.
These excessive losses due to poor optical and carrier confinement further increase
the current density evaluated above, resulting in typical thresholds of approximately
105 A/cm2 .
1.1.3
Double-heterostructure diode laser
The double-heterostructure (DH) concept solves most of the problems associated
with homojunction lasers. As illustrated in Figure 1.8, a thin active layer of undoped,
direct lower bandgap semiconductor is sandwiched between thicker n- and p-type
semiconductor cladding layers with higher bandgap energies and at the same time
lower refractive indices.
Figure 1.8 shows the structure under full forward bias leading to the injection of
large equal densities of electrons and holes into the active layer enclosed at both sides
by heterobarriers. Electrons and holes are confined in the potential well of the active
layer by the conduction band offset Ec and valence band offset Ev , respectively.
These two offsets share the difference Eg between the energy gaps of the cladding
layer and active layer: Ec = xEg , Ev = yEg , x + y = 1.
16
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.8 Schematic illustration of the carrier and photon confinement of a double heterostructure in the transverse vertical direction z of an edge-emitting diode laser. (a) Schematic
energy band edges of a strongly forward-biased laser (nearly flat-band conditions). Confinement of injected electrons (e, solid circles) and holes (h, open circles) in the potential well
of the thin, undoped active layer formed by the conduction and valence band edge energy
discontinuities Ec and Ev , respectively. (b) Refractive index profile nr (z) perpendicular to
the active layer determines the waveguiding strength of the mode in the transverse vertical
direction. (c) Field intensity profile of the fundamental optical mode in the transverse vertical
direction traveling in the axial direction x of the optical cavity.
Consequently, there are three key advantages as shown in Figure 1.8. First, the
confined carriers are forced to recombine in the thin, low-bandgap active layer to
produce optical gain. Second, the refractive index difference confines the optical
mode close to the active layer, which acts as an optical waveguide and enables a
strong overlap between the optical mode and gain region. Third, the optical mode
confinement strongly reduces the reabsorption of the laser beam in the cladding
layers and hence the intrinsic optical losses that would otherwise be very high in
the absence of index-guiding as in the homojunction laser structure. However, the
injected carriers may overflow from the active region into the surrounding cladding
layers under very high injection conditions. As we will discuss in Section 1.3.7.3,
such carrier loss via leakage over the heterobarriers will have negative effects on,
BASIC DIODE LASER ENGINEERING PRINCIPLES
17
for example, the internal quantum efficiency and the characteristic temperature T0 ,
which characterizes the temperature dependence of the threshold current.
Typical thicknesses d of the active layer are in the range of 0.1 to 0.2 μm, so
carrier densities of 2 × 1018 cm−3 required for population inversion can be achieved
at much lower currents than in homojunction lasers. The gain scales as 1/d; however,
as d decreases, the optical confinement decreases and eventually dominates over
the 1/d dependence, which is typically for d < 0.1 μm, and the gain then starts to
decrease with decreasing d. Properly optimized DH lasers have a threshold current
density of 103 A/cm2 , that is, more than two orders of magnitude lower compared
to corresponding homojunction lasers and therefore making cw room temperature
operation feasible. The dependence of the threshold gain on the active layer thickness
d will be discussed in Section 1.3.
The realization of a DH requires careful matching of the lattice constants of
the active layer and the cladding layer materials to avoid the formation of misfit
dislocations at the two interfaces due to the buildup of strong strain fields in the
case of non-matching conditions. Misfit dislocations and other defects generally
become nonradiative recombination centers with the detrimental effect of reducing the
number of injected carriers effective in the gain-building stimulated emission process.
There are two classical material systems that meet the lattice-matching condition
(within ∼0.1%) over some range of composition in each case: the GaAs active layer
sandwiched between Alx Ga1−x As claddings; and In1−x Gax Asy P1−y embedded in InP.
In addition, these material systems maintain a direct gap and enable a range of doping
levels over a certain range of composition.
The following crucial material parameters, for example, for the GaAs/AlGaAs
system, demonstrate its suitability for realizing a DH laser:
r The refractive index nr (GaAs) = 3.6 is much larger than nr (Al0.3 Ga0.7 As) =
3.4, thus the big index step of 0.2 provides strong photon confinement.
r The bandgap energy Eg (GaAs) = 1.42 eV is much smaller than
∼ 1.79 eV, which provides reduced absorption of the laser
Eg (Al0.3 Ga0.7 As) =
beam in the lossy claddings.
r The bandgap energy difference Eg ∼
= 0.37 eV leads to a conduction band
discontinuity Ec = xEg ∼
= 0.60 × 0.37 eV ∼
= 0.22 eV and valence band
∼
discontinuity Ev = yEg = 0.40 × 0.37 eV ∼
= 0.15 eV, thus providing effective carrier confinement. The 60%/40% division of the bandgap difference
is a typical ratio for the GaAs/AlGaAs system accepted in relevant technical
publications (Yariv, 1997).
Details of these material systems and others will be described in subsequent sections.
1.1.4
Quantum well diode laser
As we saw in the previous section, DH lasers consist of an active layer sandwiched
between two cladding layers with higher bandgap energy. The laser characteristics
18
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
deteriorate with decreasing thickness of the narrow-bandgap active layer, for example,
the threshold current increases because of the reduced confinement for injected
carriers and photons. However, when the thickness becomes comparable to the de
Broglie wavelength (l ∼
= h/p where p is the momentum of the electron or hole)
quantum size effects can occur resulting in profound differences in material properties
and laser performance, which will be discussed here and also in Sections 1.1.4.1
and 1.3.
Modern growth techniques, such as molecular beam epitaxy (MBE) and metal–
organic chemical vapor deposition (MOCVD), have enabled the growth of reproducible layers as thin as a few monolayers of atoms. Most high-performance
semiconductor diode lasers nowadays are based on quantum well (QW) designs
consisting of the potential well sandwiched between potential barriers with wide
bandgap energies.
Single-QW (SQW) and multi-QW (MQW) structures are employed, each with
its own specific characteristics, which will be discussed below. Lasers using QWs as
active layers with typical thicknesses of 10 nm have very reduced threshold currents.
On the one hand, this is due to the very small active volume resulting in a reduced
injection current to reach threshold (transparency); that is, a thinning of the active
layer reduces the active volume and transparency current proportionately. On the
other hand, a significant contribution to the threshold reduction can be expected from
the density of electronic states in the gain region of a QW, which is modified from
the parabolic density of states of the bulk semiconductor. We know that the density
of states for electrons of energy E in the conduction band in the three-dimensional
case is
1
Dc (E) =
2π 2
2m ∗c
2
3/2
√
E
(1.18)
where m ∗c is the conduction band effective mass, and energy E is measured from the
band edge.
In a QW with ultrathin dimension Lz and otherwise macroscopic dimensions Lx
and Ly in the QW plane, carrier motion perpendicular to the well layer is restricted and
the kinetic energy of the carriers moving in that direction is quantized into discrete
energy levels. The allowed electron wavevectors then have components kx = lπ /Lx ,
ky = mπ /Ly , and kz = nπ /Lz , where l, m, and n are integers greater than or equal
to one. The small value of Lz requires the magnitude of kz to be large. As kz can
never equal zero, there are no allowed states until kz ≥ π /Lz , or until the energy is at
least E = 2 k z2 /2m ∗c = 2 π 2 /(2m ∗c L 2z ). This is in contrast to bulk material where there
are available states beginning at the band edges Ec or Ev up to E. For a QW with
sufficiently high and wide barriers the quantized electron energy levels measured
from the conduction band edge can be approximated by
En = n2
2 π 2
2m ∗c L 2z
(1.19)
BASIC DIODE LASER ENGINEERING PRINCIPLES
19
where n is a positive integer marking the number of energy levels (Yariv, 1997).
Equation (1.19) gives the energy levels from the conduction band edge (bottom of
well), increasing inversely proportional to the square of the well thickness Lz . The
ground state of the QW is located above the band edge. A similar relation is valid
for heavy and light holes by using the relevant valence band effective masses. Figure
1.9a shows a simplified band diagram of a SQW structure illustrating the location
of the energy levels in the conduction and valence bands of the well with band
edge energy discontinuities Ec and Ev , respectively. Quantization of the energy
levels occurs only perpendicular to the well layer. In contrast, carriers are free to
move parallel to the well in the x and y directions, which leads to the known energy
versus wavevector dependencies with the bottom of the subbands corresponding to
the quantized levels. The total energy of the carriers in the well is equal to the amount
calculated according to Equation (1.19) added by the kinetic energy 2 /2m ∗ (k x2 + k 2y )
of the electrons and holes, with m∗ the relevant effective mass in the conduction and
valence band, respectively.
By calculating the number of allowed electron wavevectors per unit area in the
two-dimensional x–y plane for the nth energy level, the electron density of states in
a QW per unit volume and energy can be derived as
1
Dc,n (E) =
2π 2
2m ∗c,n
2
π
Lz
.
(1.20)
The density of states is independent of energy while at a specific value of n. In
fact, the total density of states increases by the constant amount according to Equation
(1.20) at each of the energy levels En because an electron of a given total energy E =
En can be found either in the state n or in one of the states below n, which leads to a
multiplication of the density of states, that is, a doubling at n = 2, tripling at n = 3,
and so forth. This results in the well-known staircase density of states function. A
similar treatment holds for holes in the valence bands. A plot of the density of states
comparing a SQW to a bulk semiconductor is shown in Figure 1.9a.
This staircase-like density of states significantly modifies the gain in a QW
compared to a bulk semiconductor laser. In a bulk semiconductor the states at band
edge have the highest probability of being occupied but the lowest density, which
leads to a spreading of the occupied carrier states over a large range of energies.
Consequently, the gain curve is wide and highly energy dependent, and requires a
large concentration of carriers to generate a significant population inversion. On the
other hand, in a QW the ground state already has a higher density of states, which
results in a carrier distribution with a significantly higher maximum value and a
smaller energetic width than in a bulk material. The consequences are the following:
first, a significant gain at a given wavelength can be created by a small number of
carriers; and, second, band-filling effects cause a much smaller spectral shift of the
gain curve.
The optical properties of QWs are quite different from those in a bulk semiconductor because of the quantized energy levels formed in the well. The states n = 1 in
the conduction band and valence band have the highest carrier population, because
20
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.9 (a) Simplified illustration of a single quantum well structure including the density
of states functions (solid lines) in the conduction and valence bands and the density of states
(dashed curves) in a bulk semiconductor for comparison. Schematic representation of the
corresponding quantized energy levels perpendicular to the well and the two-dimensional
parabolic bands parallel to the well. Quantized electron and heavy-hole (hh) energy levels are
shown in solid lines, light-hole (lh) energy levels in dashed lines. The most important transition
from n = 1e to n = 1hh is highlighted. (b) Calculated wavelengths of the fundamental
transition (1e–1hh) as a function of the InAs y mole fraction and well thickness Lz of a
strained Iny Ga1−y As/GaAs quantum well. Larger wavelengths are in the upper right and lower
wavelengths in the lower left of the greyscale contrast image.
BASIC DIODE LASER ENGINEERING PRINCIPLES
21
the respective quasi-Fermi function gives the highest probability of occupancy for
these states. In addition, the density of states of the heavy-hole band is larger than
that of the light-hole band. Transitions between two QW states are governed by the
overlap of the wavefunctions in these quantized states. It has been shown in relevant
textbooks (e.g., Coldren and Corzine, 1995) that, due to the orthogonality between
the QW wavefunction solutions, the overlap integral reduces such that allowed transitions can only occur between energy levels for electrons and holes with the same
quantum number n. Transitions where |n| ≥ 1 are usually forbidden. From the above
follows, that the highest optical gain will result from an n = 1 electron (1e) to n = 1
heavy-hole (1hh) transition. The total photon energy emitted in the transition is, to a
good approximation,
hν ∼
= E g,well + E 1e + E 1hh
(1.21)
where Eg,well is the bandgap energy of the well material, E1e is the electron energy of
the first quantized level with n = 1 (ground level) and E1hh is the lowest heavy-hole
energy level with n = 1.
Using the advanced commercial laser technology integrated program LASTIP
(Crosslight Software Inc., 2010), we have calculated the energy subbands of a strained
QW (cf. Section 1.1.4.1). Figure 1.9b shows the fundamental transition wavelength
l(1e–1hh) as a function of the InAs y mole fraction and well thickness Lz of a strained
Iny Ga1−y As/GaAs QW. The long wavelength l > 1 μm regime is located in the upper
right corner of the contrast image and the wavelengths around 0.91 μm in the lower
left corner. A 980 nm transition can be achieved typically for y = 0.2 and Lz = 7 nm,
which is well below the critical thickness at this composition (see the next section).
Replacing the GaAs barrier with a higher barrier material, for example, Al0.1 Ga0.9 As,
would require a larger Lz by about 1 nm in order to achieve the same wavelength for
the same well composition.
The thickness of the active layer of a QW laser is very small, typically between 5
and 10 nm. This implies that the confinement of radiation and charge capture within
a single well is very poor. Optical confinement factors in thin QWs are below 1%
and the ballistic travel distance of an injected electron is about 100 nm, which is at
least 10 times larger than a QW 10 nm thick. A large injection current would then be
required to achieve sufficient optical gain for lasing. However, these effects would
counteract the intrinsic advantage of a QW structure (high gain at low carrier density
leading to low threshold current density) resulting from the staircase density of states
function, as discussed above.
Therefore, appropriate confinement structures are used to improve carrier capture
and optical confinement to the well. Usually such structures consist of layers with
higher bandgap energy and lower refractive index sandwiching the well layer. This
structure is then surrounded by the cladding layers with higher bandgap energy and
lower refractive index than the separate-confinement heterostructure (SCH) layers.
One approach is shown in Figure 1.5b. In the wider rectangular potential well of
the SCH structure, electrons are first trapped in the SCH layer where they form a
standing wave before they cool down by phonon scattering and then drop into the
22
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
well. The optical mode is confined in the SCH layer of typically 0.2 μm thickness
with low leakage into the adjacent cladding layers and ideally negligible absorption
losses in these layers. A variation of the SCH approach is the graded refractive index
separate-confinement heterostructure (GRIN-SCH) where the index decreases and
the energy gap increases gradually within the SCH from the well to the claddings. In
addition, this structure traps the carriers, and the electric field, caused by the gradient,
drives the carriers into the well. However, compared to the SCH, this structure has a
lower density of states in the “funnel” region and therefore the carrier capture is less
effective (see Sections 1.4.1.3 and 2.1.3.3 for details in fabrication).
A second approach to resolving the problem of poor confinement in SQW structures, and which has proven to be very effective, is to use MQWs separated by thin
barrier layers, which have a lower bandgap than that of the cladding layers. Typical barrier widths are, for example, 5 nm for well thicknesses of 7 nm in a MQW
GaAs/AlGaAs structure providing substantial improvement of confinement.
The extremely large gain of QWs together with the described confinement structures has led to the achievement of very low threshold current densities. For example,
threshold current densities as low as 200 A/cm2 have been recognized as typical
values for AlGaAs/GaAs GRIN-SCH SQW lasers.
More details on gain, losses, confinement and threshold current in QW lasers can
be found in Section 1.3 along with a schematic representation of the most important
QW and confinement structures shown in Figure 1.24, including also some selected,
qualitative density of states versus energy plots.
1.1.4.1
Advantages of quantum well heterostructures for diode lasers
The use of very thin active layers in QW lasers has a series of significant consequences
leading to excellent operational features of these lasers. Some of the cw features of
these lasers will be summarized briefly as follows.
Wavelength adjustment and tunability
The wavelength can be adjusted easily by changing the well thickness Lz . It can
be evaluated, for example, for the dominating transition from the n = 1 quantized
electron state to the n = 1 heavy-hole quantized state from l = 1.24/(Eg,well + E1e +
E1hh ) by using Equations (1.19) and (1.21), where the units of the energy levels are
electronvolts and those of the wavelength micrometers.
An example may demonstrate the effect: an InGaAs/InP SQW with different Lz
values of 4, 8, and 12 nm will emit typically at wavelengths of 1.3, 1.48, and 1.55
μm, respectively (Asada et al., 1984).
As we will show in Section 1.3, a QW laser can provide a wide and flat gain
spectrum due to the onset of the n = 2 quantized state in addition to the first n = 1 state
(Mittelstein et al., 1989). Thus, lasing at shorter wavelengths of the n = 2 quantized
state was observed by decreasing the laser cavity length to increase the threshold
modal gain in a GaAs/AlGaAs SQW laser (Mittelstein et al., 1986). Also, the wide
BASIC DIODE LASER ENGINEERING PRINCIPLES
23
and flat gain spectrum enables a large wavelength tuning range. With a gratingcoupled external cavity configuration, tuning ranges of 105 nm in GaAs/AlGaAs
SQW lasers (Mehuys et al., 1989) and 170 nm in strained InGaAs/AlGaAs SQW
(Eng et al., 1990) lasers have been reported.
The wavelength range below 0.88 μm is well supported by lattice-matched DH
and QW lasers, for example, in the AlGaAs and AlGaInP material systems. Latticematched InGaAsP lasers cover the range from about 1.1 to 1.6 μm and AlGaAsSb
up to 2 μm. The range between 0.88 and 1.1 μm cannot be covered by any latticematched III–V compound semiconductor system. The gap in this important wavelength range can be filled, however, by using appropriate, strained, lattice-mismatched
InGaAs/AlGaAs QW laser systems, which are capable of accommodating elastically
the strain associated with the mismatch without forming detrimental misfit dislocations. Some details on this topic follow next.
Strained quantum well lasers
In a GaAs/AlGaAs QW the lattice constant a of the well layer GaAs is matched
to better than 0.1% that of the AlGaAs barrier. If there is a lattice mismatch a/a
between the two materials of a few percent, however, such as in InGaAs/AlGaAs,
then the introduction of misfit dislocations at the interfaces severely impacts the
proper operation of the laser. The lattice constant, for example, of In0.5 Ga0.5 As, is
larger than that of Al0.2 Ga0.8 As by as much as 3.6%. It has been shown theoretically
(Matthews and Blakeslee, 1974; People and Bean, 1985) and in many experiments
(Anderson et al., 1987; Hwang et al., 1991) that usually no defects are generated as
long as the well layer is thinner than the so-called critical layer thickness Lz,crit . The
critical thickness for In0.5 Ga0.5 As with 3.6% mismatch amounts to ∼
=5 nm and for
In0.2 Ga0.8 As with 1.2% mismatch, it is ∼
=15 nm (Anderson et al., 1987).
Figure 1.10 shows schematically the crystal lattice deformation of a well layer
with a larger lattice constant sandwiched between barrier layers with smaller lattice
constants. To accommodate the lattice mismatch and to retain approximately the same
unit cell volume, the two lattice constants must become equal in the well plane but the
lattice constant of the well must also distort in the direction perpendicular to the well
plane. This produces a biaxial compression in the well layer and a uniaxial tension
along the orthogonal direction. The well layer then loses its cubic symmetry, which
results in the removal of the degeneracy in the valence band edge and in changes
in the energies and effective masses of both heavy- and light-hole valence bands
relative to the conduction band edge (Adams, 1986; Yablonovitch and Kane, 1988)
as illustrated in Figure 1.10. The strain can be increased, for example, by increasing
the InAs mole fraction in an Inx Ga1−x As/GaAs strained-layer system, and it changes
at a rate of about 1% per x = 0.15 indium concentration in the range 0 < x < 0.5
(Coleman, 1993).
Crucial for the laser action is that the heavy-hole mass is greatly reduced under
compressive strain, with the consequence that the density of states in the valence
band becomes comparable to that in the conduction band. Both the reduced carrier
mass and the density of states in the valence band lead to a lower transparency carrier
24
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.10 (a) Simplified illustration of the crystal lattice deformation resulting from sandwiching a thin quantum well layer with an original lattice constant aw between thick barrier
layers with a lattice constant ab < aw to provide compressive strain in the well layer with
aw,s = ab,s < aw < aw,s⊥ . (b) Schematic energy versus wavenumber E–k band diagram for
an unstrained direct semiconductor showing the approximately parabolic conduction band and
degenerate heavy-hole (hh) and light-hole (lh) valence bands. The same material under biaxial
compression includes (i) the split of the degeneracy of the valence band maximum leading
to changes of the valence band masses, and (ii) the increases in the energies of both hh- and
lh-valence bands relative to the conduction band.
density and higher differential gain compared to an unstrained QW. These values
are most pronounced in the case when the effective masses in the conduction and
valence bands are equal. Ultimately, the various effects resulting from the modified
band structure will significantly raise the level of inversion in the valence band and
approach that in the conduction band, which will lead to higher gain.
This effect made possible the development of the technologically important,
strained-layer, pseudomorphic InGaAs/AlGaAs QW lasers emitting in the 900–
1100 nm band. These highly developed lasers have demonstrated excellent performance and reliability, and are mainly applied for pumping optical fiber amplifiers
and fiber lasers but are also used in various consumer applications. The 980 nm laser
is the pre-eminent component in an erbium-doped fiber amplifier, which is mainly
BASIC DIODE LASER ENGINEERING PRINCIPLES
25
deployed in long-distance optical communication systems. Chapter 2 discusses this
laser in detail.
Strained QW lasers show many desirable properties (Adams and Cassidy, 1988;
Vahala and Zah, 1988; Temkin et al., 1991; Zah et al., 1991; Tanbun-Ek et al., 1991;
Dutta, 1984) including:
r very low threshold current density due to a reduced transparency carrier density and increased electron–hole recombination time as a consequence of the
reduced transparency density;
r higher differential material gain and therefore higher differential modal gain,
which not only decreases the threshold current density, but also increases the
laser efficiency;
r lower laser linewidth;
r higher characteristic temperature T0 due to better confining potential barriers
and the lower band filling;
r mode selectivity, that is, transverse electric (TE) (electric field in the well
plane) for compressive strain and transverse magnetic (TM) (electric field
perpendicular to the well plane) for tensile strain.
Finally, it has been shown that the threshold current and lasing wavelength in a
GaAs/AlGaAs QW laser increase monotonically from compressive to tensile strain
(Tiwari et al., 1992).
In conclusion, to profit from these useful features one could design, if technically
possible, the unstrained active region of a laser such that it becomes a strainedlayer QW in the new laser device without introducing any defects affecting proper
operation.
Optical power supply
Many industrial applications of diode lasers such as pumping solid state lasers require
extremely high optical power levels, which must be available with high efficiency and
reliability. These laser sources come in single-emitter and multi-emitter devices and
are all based on QW structures. Reasons for the success of QW lasers as high-power
generators are mainly threefold:
r First, the differential gain is higher, which leads to a lower transparency current
(smaller density of states to be inverted) and hence lower threshold current.
r Second, the quantum efficiency is very high because the transparency current
(unused carrier injection) is lower in QW lasers.
r Third, the internal optical losses are much smaller in QW lasers because of the
smaller optical confinement factor than in a bulk DH laser.
These effects lead to an improved wall-plug efficiency, which is the conversion
ratio of the total electrical input power to optical output power (cf. Sections 1.3.7.1
26
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
and 2.4.5.3). The consequence is less heating of the device, which improves the laser
performance by effectively increasing the optical output power and laser reliability
by increasing the catastrophic optical damage level (see e.g. Chapters 3 and 4).
Temperature characteristics
From an application point of view, the temperature dependence of the laser characteristics is very important. The optical output power of a diode laser decreases at
constant current operation with increasing temperature. Temperature characteristics
determine the performance and reliability of a diode laser. The optical output power
gradually decreases with temperature because of the increase in threshold current and
decrease in laser efficiency, which can be expressed empirically by separate, similar
exponential dependencies on temperature (Hayashi et al., 1971), see Section 1.3 for
details. The characteristic temperature T0 is a measure for the temperature dependence of the lasing characteristics. This characteristic temperature for the threshold
current usually decreases as the ambient temperature increases and a large T0 indicates a small change in lasing characteristics with temperature (the latter is highly
desired for most applications).
In general, T0 of QW lasers is higher than that of bulk active layer lasers, which is
caused by the lower threshold current density and reduced carrier overflow from the
wells into the adjacent layers (O’Gorman et al., 1992). At higher threshold currents,
higher lasing energy levels are populated due to the increased injected carrier density,
which leads to an increase in the quasi-Fermi levels and, consequently, an increased
electron escape rate.
More details on the physical mechanisms responsible for the temperature characteristics will be given in Section 1.3.7.3 along with T0 data for different QW structures
and material systems.
1.1.5
Common compounds for semiconductor lasers
The performance of a semiconductor laser depends sensitively on the intrinsic properties of the materials used in the design and fabrication. The most critical parameters
to be considered in the selection of appropriate materials are both the bandgap energy,
which determines the lasing wavelength, and the lattice constant, which is responsible
for a defect-free interface between two semiconductors with different bandgaps. To
reduce the formation of lattice defects, which can strongly impact the performance
and reliability of a laser, the lattice constants of the different layers in the vertical
structure should typically match to better than 0.1%. As we saw in the last section,
the lattice constant requirement is slightly relaxed in a strained-layer system in that a
small lattice mismatch of 3% can be tolerated up to a certain critical layer thickness
of typically <15 nm without the formation of any defects.
Considering the bandgap and lattice constant conditions to be met by the many
layers involved in a structure – at least three for a DH device and, in more complex
structures such as SCH QWs, at least five layers – it seems that there is only a
BASIC DIODE LASER ENGINEERING PRINCIPLES
27
very limited set of semiconductors available that meet all the material specifications
required to make a high-quality diode laser according to the application requirements.
However, as Figure 1.11 shows, potential semiconductor materials for optoelectronic devices comprise binary, ternary, and quaternary III–V compound semiconductors. Mixing different kinds of binary compounds creates a new compound with
properties intermediate between those of the original ones. The properties of the new
compound vary linearly in proportion to the alloy composition according to Vegard’s
law (Vegard, 1921; the paper is discussed in many semiconductor textbooks). This
procedure works well for lattice constants as long as the linear interpolation occurs
Figure 1.11 Bandgap energies and lattice constants of common III–V compound semiconductors used for high-power diode lasers. Compound binaries are represented as solid dots and
ternaries as solid lines. Dashed lines represent regions of indirect gap. In1−x Gax Asy P1−y (clear
region with thick solid lines) and (Alx Ga1−x )y In1−y P (light grey region) are obtained by varying
compositions x and y. The two dot–dashed vertical lines show the range of bandgap energies
of ternaries and quaternaries that can be grown lattice-matched on the binary substrates GaAs
and InP. Some specific ternaries are depicted. For comparison ZnSe (♦), Si (), Ge (), and
PbS (×) are also shown.
28
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
in the direct bandgap regime of the new compound. For the evaluation of other parameters, such as the bandgap, a second-order bowing parameter must be added to
improve the value of the weighted average. Examples for a ternary are Alx Ga1−x As
made up of the binaries GaAs and AlAs, and for a quaternary In1−x Gax Asy P1−y with
GaAs, GaP, InAs, and InP as the constituents.
Figure 1.11 illustrates the correlation between bandgap energy and lattice constant
for different binary, ternary, and quaternary compound semiconductors (Kressel and
Butler, 1977; Casey and Panish, 1978). The emphasis here is on materials enabling
laser emission in the wavelength range of approximately 0.63–1.55 μm where the
highest optical output powers have been demonstrated. This range includes important
wavelengths, such as at 1.31 and 1.55 μm used in optical fiber communications, 0.98
and 1.48 μm for pumping fiber amplifiers, 0.81 μm for pumping Nd:YAG due to
the excellent match to its absorption spectrum, and wavelengths between 0.63 and
0.78 μm for optical data storage, laser printers, and machining. Most of these materials
have a direct bandgap in E–k space, which is a decisive condition for using them in
the development of high-power diode lasers. Relevant features of these materials are
discussed below. Regarding relevant laser power values, see e.g., Tables 1.2 to 1.5,
Sections 1.2.5 and 2.1.3.3.
r Alx Ga1−x As can be grown on GaAs lattice-matched to better than 0.1% and
it can be grown for any value of x without introducing defects due to lattice
mismatch. However, only for x < 0.45 is it direct; for higher values it has
an indirect gap. The x dependence of its energy gap can be approximated by
Eg (x < 0.45) = (1.424 + 1.247x) eV (Casey and Panish, 1978). The band
offsets in the conduction and valence bands split to about 60% to 40% for
AlGaAs/GaAs, respectively (Yariv, 1997). Lasing wavelengths are typically in
the range of 700 to 900 nm for DH structures.
r The wavelength regime of 900–1100 nm can only be covered by the strainedlayer system Inx Ga1−x As sandwiched between AlGaAs or GaAs layers as
discussed in the last section. The indium ion is larger than the gallium ion and
therefore InGaAs has a higher lattice constant than GaAs with the consequence
that InGaAs is under compressive strain. For layer thicknesses below a critical thickness the mismatch strain can be accommodated elastically without
forming misfit dislocations, and the resulting biaxial compression modifies
the valence band structure of InGaAs such that efficient inversion now occurs
also in the valence bands leading to increased gain. A typical band offset ratio is Ec /Ev ≈ 80%/20% (Arias et al., 2000). The lasing wavelength can
be controlled by changing the thickness and indium mole fraction of the thin
strained InGaAs QW layer (cf. Figure 1.9b). The same wavelength range of
900 to 1100 nm can also be obtained by using a strained InGaAs QW sandwiched between InGaAsP SCH and In0.49 Ga0.51 P cladding layers. This system
is aluminum-free and consequently has improved laser operation (Botez et al.,
1996; Mawst et al., 1996) (see Section 2.1.3.3 for laser properties in this
material system).
BASIC DIODE LASER ENGINEERING PRINCIPLES
29
r In1−x Gax Asy P1−y grown on InP is the classical material system delivering
wavelengths for long-distance fiber optic communications in the range of 1.1
to 1.65 μm by changing the mole fractions x and y accordingly. Wavelengths
at 1.3 and 1.55 μm are of particular interest, where the standard silica fiber has
minima in total dispersion and loss, respectively. A range of lattice-matched
quaternaries extending from InP to the InGaAs ternary line can be grown
by complying with the mole fraction condition x = 0.4y + 0.067y2 . Direct
bandgap energies can be achieved ranging from 0.75 eV for the ternary endpoint In0.53 Ga0.47 As to 1.35 eV for InP. Compared to AlGaAs/GaAs, the band
offsets in this system are quite different: only 40% of the band offset is in the
conduction band, whereas the band offset in the valence band of 60% is much
higher (Piprek et al., 2000). In contrast, the InGaAlAs on InP material system
delivers higher band offsets in the conduction band leading to lower electron
leakage and improved laser characteristics (Zah et al., 1992).
There is an approach to extend GaAs-based lasers with all their positive
characteristics, including high-temperature operation (high T0 ), to 1.3 μm and
to replace InGaAsP lasers with their thermal problems (low thermal conductivity, high electron escape due to low conduction band offset). This has been
achieved by InGaAsN/GaAs QW structures with the incorporation of only a
very low N content of <2% to avoid a strong degradation of luminescence
efficiency at higher concentrations (Kondow et al., 1996, 1997). Excellent
laser characteristics have been reported, including threshold current densities
down to 500 A/cm2 from narrow-stripe (∼4 μm) devices 350 μm long, lasing
wavelengths between 1.24 and 1.3 μm, and reliable cw operation up to at least
100 ◦ C with high characteristic temperatures T0 of 110 K (Borchert et al., 2000;
Riechert et al., 2000). The latter is caused by the high confinement energy for
electrons in these structures, which is due to (i) the high conduction band
offset of about 80%, and (ii) the increased electron mass compared to InGaAs
(Hetterich et al., 2000; Shan et al., 1999). The higher electron mass, however,
leads to transparency current densities roughly three times higher than for
980 nm InGaAs QW lasers.
r AlGaInP diode lasers are now well established to cover roughly the wavelength
range of 600 to 700 nm in the visible red. Gax In1−x P has a direct energy gap for x
up to about 0.7 and an indirect gap at higher values of x. At x = 0.51 the material
is lattice-matched to GaAs (Casey and Panish, 1978), which is therefore the
preferred substrate. The substitution of Ga by Al produces hardly any change in
the lattice constant because the ion sizes are approximately the same. Therefore,
with the indium mole fraction fixed at 0.49, Ga may be partially replaced
by Al to provide various bandgap energies while maintaining a fixed lattice
constant matching GaAs. The resulting quaternary then has the composition
(Alx Ga1−x )0.51 In0.49 P, which is a direct gap material for Al fractions x up to
about 0.7. Strain can be produced in a thin GaInP layer by changing the In/Ga
ratio, where compressive strain results from an increased In content and tensile
strain from an increased Ga content. A higher In content leads to a reduced
30
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
bandgap but increases both the optical and carrier confinement. A Gay In1−y P
QW layer sandwiched in (Alx Ga1−x )0.51 In0.49 P separate confinement barrier
layers is lattice-matched for y = 0.51 and compressively-strained for y < 0.51.
Threshold current densities of about 200 and 700 A/cm2 have been reported for
compressively-strained SQW lasers emitting near 690 nm (Katsuyama et al.,
1990) and 632 nm (Valster et al., 1992), respectively.
Appropriate materials to cover the wavelength regime l > 1.6 μm are III–V,
II–VI, and IV–VI (lead salts) semiconductor compounds and alloys (Eliseev, 1999).
Typical representatives are InGaAsSb, HgCdTe, and PbSnTe, respectively. However,
output powers of lasers made of these material systems are relatively low, and in
the case of lead salts even low-temperature operation of the lasers emitting in the
far-infrared region of 3–34 μm is required. Figure 1.11 shows the direct gap, binary
compounds InSb and GaSb, which form together with InAs the alloy InGaAsSb
successfully developed for commercial diode laser and photodiode applications.
Lattice-matched QW layers of Inx Ga1−x Asy Sb1−y embedded in
Alx Ga1−x Asy Sb1−y barriers have been grown on GaSb substrates and can
cover the wavelength range of 1.7 to 4.4 μm. The lowest room temperature threshold
current density was 260 A/cm2 achieved for long (1000 μm), broad (100 μm), and
low optical loss (10 cm−1 ) lasers emitting a cw output power up to 190 mW/facet
(Choi and Eglash, 1992). (AlGaIn)(AsSb) QW broad-area lasers and linear laser
arrays (20 emitters on a 1 cm long bar) emitting in the range of 1.9 to 2.2 μm have
achieved typical cw output powers of 2 and 20 W, respectively (Kelemen et al.,
2008).
Material systems used for short wavelengths in the green, blue, and ultraviolet
(UV) regime are II–VI compounds and III–V nitride systems, but they are not shown
in the figure. Classical representatives in the former group are ZnS, ZnSe, and ZnSSe.
However, heterojunction systems made from these materials suffer usually from high
charge carrier escape, in particular electron loss, due to a much lower bandgap
difference in the conduction band than in the valence band caused by the relatively
high ionicity of these semiconductors. Doping with Cd can reduce the carrier loss
by lowering the bandgap, which, however, increases the emitting wavelength. An
important material, especially useful for the claddings, is MgZnSSe, which has a
wide gap of about 3.5 eV and can be grown lattice-matched to GaAs or ZnSe.
In general, the refractive indices and refractive index differences in these material
systems are lower than in the standard III–V semiconductors, resulting in lower
optical confinement.
The other group of materials comprises III–V nitrides with the basic binaries GaN
and AlN, which are direct semiconductors of very large bandgap energies of 3.4 and
6.2 eV, respectively. In contrast to the AlGaAs system, the incorporation of Al to GaN
causes a reduction in the lattice constant by about 2.4%. The addition of In to GaN
shifts the wavelength from the UV to the visible and increases the lattice constant
by about 11%. Because of the high ionicity of the nitrides, the refractive indices are
even lower than in the previous II–VI materials. By adjusting the composition and
BASIC DIODE LASER ENGINEERING PRINCIPLES
31
doping, however, effective waveguiding can be achieved. For a long time effective
technological progress was hampered by the mismatch in lattice constants and thermal
conductivities between nitride layers and substrates. A recent breakthrough has been
achieved by using a triple In0.07 Ga0.93 N/In0.01 Ga0.99 N QW sandwiched in a GaN
SCH and AlGaN claddings, which were deposited on an n-type GaN substrate. Ridge
waveguide lasers 7 μm wide, 600 μm long, and with cleaved uncoated facets emitted
with high efficiency at room temperature record-high cw output powers up to 2 W
at a wavelength of 405 nm and operating currents and voltages up to 1 A and 5.7 V,
respectively (Saito et al., 2008).
Table 1.1 summarizes the material systems described above, and includes common cladding/active layer structures grown on appropriate wafer substrates, typical
lasing wavelength ranges for each material system, and wavelength-dependent applications grouped in four blocks.
1.2
Optical output power – diverse aspects
1.2.1
Approaches to high-power diode lasers
Edge- and surface-emitting lasers are the two fundamental concepts for implementing
semiconductor diode lasers.
1.2.1.1
Edge-emitters
Edge-emitters have mirror facets that are perpendicular to the surface of the wafer
substrate and the optical mode propagates parallel to the surface of the wafer (see
Figure 1.1 and Section 1.1.1.3 above). These devices can be classified roughly into
the following groups consisting of single-emitters and multi-emitters including:
r Narrow-stripe devices of typically 3–5 μm widths delivering kink-free, high
output powers in the 1 W range in a single transverse vertical and lateral mode
reliably up to high drive currents (see Sections 2.1 to 2.3).
r Broad-area lasers with typically 100 μm widths supplying output powers up to
25 W in a single spatial mode under certain design conditions (see Section 2.4).
r Tapered amplifier lasers including tapered unstable resonator lasers and monolithically integrated master oscillator power amplifiers (MOPAs), which comprise a single-mode laser and a flared-contact (with a typical width from 4 to
250 μm) power amplifier, are capable of delivering the highest diffractionlimited, single-mode output in the 12 W cw range (see Section 2.4).
r Laser array bars, which come in two forms. First, phase-locked, anti-guided
arrays deliver coherent powers in narrow, diffraction-limited beams (cf. Section
1.2.2) in the 1 W cw range from, for example, 20 closely spaced, single emitters
120 μm wide in the bar. Second, spatially incoherent arrays with a laser bar
1 cm long as the basic building block achieve today the highest optical power
32
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Table 1.1 Key diode laser material systems including typical cladding/active layer
configurations, substrates, lasing wavelength ranges and major applications in each of the
four groups.
Substrate
Wavelength
[μm]
typ. x ≅ 0.02–0.30
SapphireGaN
buffered
~ 0.35–0.50
CdxZn1−xS/CdS 2)
CdS
~ 0.35–0.50
GaAs
~ 0.60–0.70
GaAs
~ 0.70–0.92
Cladding/active layer
GaN/InxGa1−xN 1)
(AlxGa1−x)0.5In0.5P/GayIn1−yP
x = 0.7: T0 high, Jthr low
y = 0.5 latt. match. y < 0.5 comp. strain
AlxGa1−xAs / GaAs
x < 0.45 (direct gap)
AlxGa1−xAs/InyGa1−yAs comp. strain
Practical ranges: y ~ 0.08–0.42, x ~
0.20–0.85, Lz ~ 7–15 nm. Jthr minimum
for y ~ 0.2, x ~ 0.35, Lz ~ 8 nm
GaAs
~ 0.90–1.10
InP
~ 1.1–1.65
GaAs
~ 1.24–1.30
InP/GaxIn1−xAsyP1−y
x ~ 0.47y: l. m. to InP. Endpoint
In0.53Ga0.47As. λ = 1.3 (1.55) μm: x ~
0.28 (0.37), y ~ 0.6 (0.8)
AlxGa1−xAs/InyGa1−yAs1−xNx 3)
λ = 1.3 μm for active: x = 0.017, y =
0.35; cladding: x = 0.3; Lz ~ 7 nm
AlxGa1−xSb1−yAsy/
InxGa1−xSb1−yAsy 4)
For λ = 2.2 μm (lattice-matched layers):
Active: x = 0.16, y = 0.14
Cladding: x = 0.75, y = 0.06
GaSb or
InAs
~ 1.70–4.40
Major
applications
Holographic storage.
Image recorders, fax
machines, printers.
Pumping solid state,
e.g., Nd:YAG at 810
nm and fiber lasers.
Barcode readers. Bluray discs, HD DVD,
opt. ROM (780 nm).
Materials processing.
Printing, graphics arts.
Medical therapeutics.
Aerospace, military
systems, rangefinders
Telecommunications.
Fiber amplifier pumps.
Materials processing.
Medical therapeutics
Fiber optics
communications [silica
fiber low dispersion
(loss) at 1.3 (1.55)
μm], transceivers,
Raman amplifiers.
Aerospace, military,
rangefinders
Spectroscopic sensing
of humidity, gas
impurities, drugs. Next
gen. of fiber-optics
comms. based on
novel fluoride, sulfide
glasses with very low
losses ~ 10−3 dB/km at
2.4 μm range
Typ. blue/UV diode lasers. Record -high powers: 2 W of 7 μm wide lasers 1) ; Saito et al.,
2008. 3) Potential alternative to InGaAsP: higher material gain and conduction band offset,
higher T0 (126 K) (Kondow et al., 1996, 1997; Borchert et al., 2000; Riechert et al., 2000).
4)
λ = 1.9–2.2 μm: 100 μm MQW laser with 190 mW cw/facet at 300 K (Choi and Eglash,
1992); 2 W cw for BA lasers, 20 W cw for 1 cm laser bars (Kelemen et al., 2008).
1) , 2)
BASIC DIODE LASER ENGINEERING PRINCIPLES
33
Figure 1.12 Simplified diagrams of basic edge-emitting diode laser structures (top views;
effective active gain regions shown in hatched patterns; mirrors: high-reflectivity (HR), antireflectivity (AR), low-reflectivity (LR) distributed Bragg reflector (DBR)): (a) narrow-stripe
device; (b) broad-area device with wide aperture; (c) tapered device utilizing a single-mode
(SM) laser and a flared-contact power amplifier; (d) unstable resonator laser approach with
curved mirror facet; (e) monolithic diode laser array bar structure.
up to 1 kW cw from a single monolithic laser chip having a filling factor of up
to 80% (ratio between pumped and unpumped area of bar) and an electricalto-optical power conversion efficiency as high as 70% (see Section 2.4 for
details).
Figure 1.12 shows simplified, schematic illustrations of these four laser types in
top view. Specific design issues and performance figures of these high-power, singlemode, diffraction-limited laser approaches and other conceptual techniques such as
unstable resonator designs (see Figure 1.12) with large emitting curved apertures,
and tapered lasers, will be discussed in detail in Section 2.4.
1.2.1.2
Surface-emitters
In surface-emitting devices, the laser output is normal to the surface of the wafer.
These devices come in two categories. In one category there are lasers, which have
34
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
their optical cavity normal to the wafer. These devices are known as vertical-cavity
surface-emitting lasers (VCSELs). The other class comprises lasers where the active
layer has the conventional waveguide structure but the laser beam is deflected normal
to the substrate surface using (i) a 45◦ etched output mirror, (ii) a folded cavity
realized with a 45◦ deflecting intracavity mirror or bent-waveguide structure, or (iii)
a diffraction grating, which is etched on the top p-type cladding layer and couples
the light out vertically to the surface (Iga and Koyama, 1999).
VCSEL devices have very short cavity lengths in the micrometer range, which
would imply extremely high mirror losses. To counteract this negative effect and
to decrease the threshold gain, which is inversely proportional to the cavity length,
the reflectivity of the mirrors must be close to 100%. This can be realized by using distributed Bragg reflectors (DBRs) composed of a semiconductor multilayer
structure consisting of a series of alternating, high and low refractive index layers
a quarter of a wavelength thick (see also Section 1.3.8). Reflectivities of more than
99% can be achieved, for example, with 20 pairs of an epitaxially grown GaAs/AlAs
DBR. The very short cavity leads to very large mode spacing and therefore only a
single longitudinal mode is excited in the spectral gain regime. A cross-sectional
view of the concept of a VCSEL is illustrated in Figure 1.13. VCSELs have become a maturing technology that has been successfully commercialized by many
companies for applications such as parallel processing of information or parallel optical interconnection between computers. They have attractive features including a
low-divergence circular output beam, temperature-insensitive output characteristics,
high-speed modulation capability at low driving currents, submilliamp threshold currents, wafer-scale fabrication, and on-wafer testing. These high-performance devices
have the desired circular output beam but their single-mode output power is limited
to ∼10 mW cw for device diameters <10 μm. For larger device diameters >100 μm
Figure 1.13 Schematic illustration of the vertical-cavity surface-emitting laser (VCSEL)
approach with an oxide current confinement layer. The laser cavity is perpendicular to the
substrate plane and the mirrors of the resonator consist of distributed Bragg reflectors (DBR)
with high reflectivities close to 100%. The length of the laser cavity is short, typically in the
range 1–3 μm.
BASIC DIODE LASER ENGINEERING PRINCIPLES
35
the power can be around 200 mW cw; however, the output beam then has multiple
transverse modes.
Vertical external cavity surface-emitting lasers (VECSELs) make use of the
VCSEL design and offer a technologically important concept to increase output
power and beam quality directly in a vertical resonator device. These devices use a
three-mirror, coupled cavity design comprising the active region sandwiched between
the p-doped, high reflectivity R > 99% Bragg reflector at the bottom, the n-doped
Bragg reflector with a partial transparency at the top, and the curved external mirror.
Electric current is injected through a circular p-aperture at the bottom, while the
n-contact has an anti-reflection-coated circular aperture to allow the beam through
to the external mirror. The p-mirror is soldered to the heat sink for efficient heat
removal. The shape and size of the external mirror control the power and transverse
mode operation, whether the laser operates in multi-mode or in a single fundamental
mode. Electrically pumped VECSELs emitting at 980 nm have generated 1 W cw
multi-mode and 0.5 W cw in a fundamental TEM00 mode and single frequency with
90% coupling efficiency into a single-mode fiber (McInerney et al., 2003).
Surface-emitting structures have also been used to fabricate high-power laser
arrays, which can be designed such that neighboring emitters in the array oscillate in
phase, that is, the phase of the optical field of an emitter is synchronized with those of
the other emitters in the array. This leads to a sharp emission including a single-lobe
far-field pattern (Chang-Hasnain, 1994).
1.2.2
High optical power considerations
There is no exact definition of the power value necessary to call a diode laser a laser
with high power, but it is generally accepted that levels above 100 mW for narrowstripe, single-mode devices and above 1 W for all other single- and multi-emitter
lasers can be considered to be high power. Lasers with low powers in the range below
10 mW serve many applications, including 780 nm GaAs lasers used in compact
disc (CD) players, 670 nm AlGaInP lasers in barcode scanners, and 1.3 and 1.5 μm
InGaAsP single-mode lasers in optical communication systems. In contrast, highpower lasers have different applications depending on the operation of the laser. For
example, to pump solid state lasers the focus is only on the highest possible power,
which can be achieved, for example, by a laser array.
High powers as well as near diffraction-limited, coherent laser beams are crucial
for applications such as optical recording, printing, frequency doubling, free-space
communication, laser tweezers, and fiber amplifier pumping with the requirements
of transmitting the light over long distances or focusing the beam to a very small
spot of high-power density. Excellent examples of such application-tailored lasers
are the kink-free, single-mode, fiber-coupled power levels of 750 mW achieved from
narrow, ridge-waveguide, strained-layer InGaAs/AlGaAs SQW lasers emitting in the
980 nm band for pumping erbium-doped fiber amplifiers used in long-haul fiber optic
communication links (Bookham, Inc., 2009). In this context, it is important to note
the significance of the brightness of a laser.
36
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
1.2.2.1
Laser brightness
The maximum peak intensity, which can be obtained by focusing a laser beam, is
proportional to the beam brightness, and the brighter the laser, the further the distance
that energy can be propagated. The brightness of a given laser source cannot be
changed and is independent of the optical system that follows the source. Brightness
B is given by the power P emitted per unit solid angle per unit area and is measured in
units of W sr−1 cm−2 . B is defined as B = P/(dθ ⊥ Dθ ), where d is the maximum extent
of the near-field in the mirror plane normal to the active layer, D is the maximum
extent parallel to the active layer, and θ ⊥ and θ are the full-width, half-maximum
(FWHM) points of the far-field divergence angles measured in radians in the direction
normal (fast-axis) and parallel (slow-axis) to the active layer.
For a diffraction-limited laser output (θ ⊥ = l/d, θ = l/D) we obtain the brightness B = P/l 2 . The brightness of a laser is orders of magnitude higher than that of a
spatially incoherent light source of similar power. The brightness of a 1 W, 980 nm
laser can be calculated to be about 1 × 109 W sr−1 cm−2 , and hence is seven orders
of magnitude larger than that of a high-pressure mercury-vapor lamp emitting about
10 W at 546 nm. The same ratio is also obtained for the two peak intensities by focusing the beams of the two sources. These figures demonstrate the importance of using
focused, high-brightness laser beams in industrial material processing applications
such as welding, cutting, marking, drilling, and so forth.
1.2.2.2
Laser beam quality factor M2
The beam quality factor M2 , also called the beam propagation factor, characterizes
the degree of imperfection and focusing ability of a laser beam. It compares the
characteristics of a real beam to those of a pure fundamental TEM00 mode, that
is, M2 = 1 for a diffraction-limited Gaussian beam. The closer M2 is to 1.0, the
better the beam can be focused. For any other beam M2 > 1. This factor relates the
divergence of a real laser beam in the far-field to its near-field waist size (Siegmann,
1990, 1993).
According to the ISO 11146 standard (ISO, 2005), the relationship between M2 ,
wavelength l, near-field beam waist (minimum spot size) w0 , and beam divergence
half-angle θ is given by M2 = θ w0 /(l/π ). As l/π w0 is the diffraction-limited angular
divergence of a Gaussian beam, therefore M2 is a single number. The quality factor
M2 of a real laser beam describes the deviation from a theoretical diffraction-limited
Gaussian beam with M2 = 1 and is always ≥1.
M2 is measured by focusing the laser beam and measuring several beam profiles
along the beam caustic. The divergence angle is determined by θ = df /f where df
is the beam diameter at the focal distance f of the lens used. Thus, to evaluate M2
it is necessary to measure both the near-field and far-field beam waist. Commercial
instruments are available for measuring M2 in real time. The M2 formalism offers a
convenient way to define in one single number the quality of a laser beam, which can
have, for example, distorted, multimode, or partially incoherent characteristics. The
M2 factor can be very different for elliptical laser beams such as in broad-area lasers
BASIC DIODE LASER ENGINEERING PRINCIPLES
37
or diode laser bars (Chapter 2). In these lasers, M2 is much larger in the transverse
lateral (slow-axis) than in the transverse vertical (fast-axis) direction.
1.2.3 Power limitations
As we will see in one of the following sections, the output power of a diode laser
is measured by the optical power output (P) as a function of the drive current (I)
input characteristic P/I. In an ideal case, the P/I curve is a straight line with a slope
corresponding to an ideal efficiency of one emitted photon per injected electron.
However, in reality the characteristics look different and the useful power levels can
be impacted by roughly four factors including (i) the appearance of kinks in the P/I,
(ii) power rollover with increasing current, (iii) catastrophic optical damage, and (iv)
aging effects. Figure 1.14 shows a schematic representation of these effects.
These performance-degrading effects will be described in detail in subsequent
sections and chapters. In the following, however, a short summary should illustrate
the physical processes leading to these effects.
1.2.3.1
Kinks
In general, multimode operation of the laser is the cause of the occurrence of a
discontinuity (kink) in the P/I curve, which is the most common mechanism limiting
the effective power for single spatial mode radiation. The excitation of higher-order
spatial modes causes a distortion of the far-field radiation pattern and a deviation
from the ideal Gaussian-like shape, which is reflected at the onset of modes higher
than the fundamental mode. The physical origin for the excitation of these additional
modes can be seen in the perturbation of the designed waveguide refractive index or
gain profile, which is caused by nonuniformities in the local carrier population and/or
Figure 1.14 Limitations of useful diode laser optical output power illustrated schematically
(a) in power (P) versus current (I) characteristics: (1) ideal output, (2) kink, (3) catastrophic
optical damage (COD) at mirrors or in cavity, (4) thermal rollover; and (b) during aging power
versus time: (1) gradual degradation, (2) sudden (COD) power degradation.
38
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
temperature. P/I curves with a kink are usually reversible. Details of the kink issue
will be discussed in Section 1.3 and Chapter 2.
1.2.3.2
Rollover
The characteristic of this effect is the continuous decrease in laser efficiency (power
increase per current unit) with increasing current. This is due to Ohmic losses, which
increase at higher injection currents and lead to higher heat powers dissipated in the
proximity of the p–n junction. The resulting increase of the active layer temperature
leads to a reduction of the internal quantum efficiency (see Section 1.3) with the
effect that the power level ultimately saturates, and eventually decreases (rolls over)
with increasing current. The actual reason for this effect is carrier escape from the
active region into the adjacent cladding layers where the carriers cannot contribute
to population inversion and gain. Ineffective carrier confinement and insufficiently
high band offsets are responsible for this carrier loss. The optical output can finally
diminish to close to zero for very high temperatures, leading to a collapse of the laser
gain. Thermal rollover is usually a reversible event and it is the main power-limiting
mechanism in: (i) 1.3–1.5 μm InGaAsP/InP lasers, which have poor temperature
characteristics due to low band offsets and high nonradiative Auger recombination
processes; and (ii) diode lasers with high thermal resistance. Section 1.3 presents
more details on the thermal rollover effect.
1.2.3.3
Catastrophic optical damage
Catastrophic optical damage (COD) is an irreversible process, which can occur at
laser mirror facets and in the bulk of the cavity of the laser by strong heating due
to high optical power densities and/or nonradiative carrier recombinations. COD at
mirrors, also called COMD, is the result of strong surface recombination via traps,
which causes a depletion of charge carriers at the crystal surface. The depleted
bands of the active region now become absorbing at the lasing wavelength. The heat
generated in this process raises the local temperature very strongly. At a critically
high optical flux density, the raised temperature causes a sufficient shrinkage of the
local bandgap energy such that the optical absorption becomes even higher. This
positive feedback can cause a thermal runaway with ultimately melting of the end
facet of the laser, irreversibly diminishing any useful laser output power. COD is
especially prevalent in aluminum-containing semiconductors and as a result strongly
impacts the reliability of AlGaAs lasers. However, the application of appropriate
facet passivations and coatings (see Chapters 3 and 4) greatly increased the COMD
level by at least one order of magnitude compared to untreated mirrors and which is
currently higher than 100 MW/cm2 for the leading, narrow-stripe 980 nm pump laser
on the market (Lichtenstein et al., 2004; Bookham, Inc., 2009).
COD events in the cavity are due to the generation and growth of so-called
dark-line defects (DLDs), which are regions with greatly reduced radiative efficiency.
The main origins of a DLD are threading dislocations originating from defects in
the wafer substrate, and stacking faults introduced during the epitaxial growth of
BASIC DIODE LASER ENGINEERING PRINCIPLES
39
the active region layers. These dislocations can grow into networks by nonradiative
recombination processes with a growth rate promoted by the presence of mechanical
strain and thermal gradients. The formation of DLDs is also sensitively dependent
on the material system, and is much more pronounced in AlGaAs/GaAs than in
InGaAsP/InP lasers. A DLD can act as a sink for injected carriers and as an absorber
of laser light in the cavity. These effects can cause a rapid degradation of laser performance with final catastrophic failure in the active region due to strong Joule heating.
COD-related phenomena and effects will be discussed in detail in Chapters 3–9.
1.2.3.4
Aging
The operation of a diode laser at constant drive current and temperature over a long
period of time usually leads to a reduction in optical output power. The strength
and type of the transition to lower powers depend sensitively on the laser structure,
materials, fabrication technology, and operating conditions as well as the type of
root causes involved. In brief, thermal dissipation, high current density, and rapid,
catastrophic-like optical damage events are the major reliability-limiting factors. As
we saw in the last paragraph, thermal and carrier-induced degradation mechanisms
are linked to the formation of extended lattice defects, which can migrate and grow in
the active region with the effect of reducing the optical power over time. Chapters 3
and 4 describe the fundamental diode laser degradation mechanisms. Chapters 5 and
6 discuss basic reliability engineering concepts and techniques, and describe a diode
laser reliability test program required to achieve qualification of a laser product.
1.2.4
High power versus reliability tradeoffs
Depending on the specific laser application, there are certain tradeoffs to be considered
to achieve laser operation at high optical power and high reliability (Mehuys, 1999).
There are three different cases to be taken into account:
r Case 1: Reliability is limited by the optical power density at the output facet.
Then a reduction in the optical overlap of the active region can be applied to
increase the COMD level.
r Case 2: Reliability is limited by heat dissipation. Then an increase in the optical
overlap of the active region may help to lower the threshold current density
and increase the electrical-to-optical power conversion efficiency.
r Case 3: Reliability is limited by the current density in the semiconductor. One
solution would be to increase the effective active region area, which lowers
the current density at a fixed total drive current. A second solution could be to
lower the drive current by adjusting the optical overlap of the active region. In
a third solution the external differential quantum efficiency could be increased
by adjusting the mirror reflectivities (see Section 1.3.8).
40
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
1.2.5
Typical and record-high cw optical output powers
1.2.5.1
Narrow-stripe, single spatial mode lasers
Table 1.2 lists state-of-the-art, cw, optical output powers of narrow-stripe, single
spatial mode diode lasers as a function of the lasing wavelength. The values given
are for selected commercial laser products and research devices from the UV to the
mid-IR. Figure 1.15 shows the power data of the table plotted as a function of the
lasing wavelength. Two results stand out and are worth looking at closer regarding
the design and technology used.
First, the Toshiba Research Group (Saito et al., 2008) succeeded in fabricating
GaN-based, ridge waveguide lasers 7 μm wide with the highest power characteristics
at a wavelength of 405 nm and at room temperature. The devices emitted typical
cw powers of 2 W at 1 A operating current and 5.7 V operating voltage with a high
slope efficiency of 2.6 W/A. This device is not included in Figure 1.15 because no
direct or indirect information is available whether the laser emitted in single spatial
mode or not; however, we consider the technology as sufficiently advanced to be
reported here. The triple 3 nm In0.07 Ga0.93 N/10 nm In0.01 Ga0.99 N QW/barrier stack is
sandwiched in a 100 nm GaN SCH layer with adjacent AlGaN cladding layers grown
practically lattice-matched on an n-type GaN substrate.
Table 1.2 State-of-the-art, continuous wave (cw), optical output powers of
narrow-stripe, single spatial mode diode lasers as function of the lasing
wavelength from the ultraviolet to mid-infrared regime. Selected products and
research devices (status 2009).
Wavelength
[nm]
Cw power
[mW]
Company/institution
375
405
405
450
488
515
640
660
785
808
850
915
980
1060
1300
1400–1480
1510
2300
2500
20
470
2000 (7 μm ridge)
80
60
5
250
130
150
200
200
300
750 (ex-fiber)
852
600 (ex-fiber)
710 (ex-fiber)
320 (ex-fiber)
30
20
Nichia (2009)
Ryu et al. (2006)
Saito et al. (2008)
OSRAM (2009)
Nichia (2009)
Nichia (2009)
opnext (2009)
Mitsubishi Electric (2009)
opnext (2009)
SANYO (2009)
Frankfurt Laser (2009)
opnext (2009)
Bookham (2009)
Zah et al. (2004)
Garbuzov et al. (2002)
Garbuzov et al. (2001)
JDSU (2009)
Frankfurt Laser (2009)
Frankfurt Laser (2009)
BASIC DIODE LASER ENGINEERING PRINCIPLES
41
Figure 1.15 State-of-the-art, continuous wave, optical output powers of narrow-stripe, single
transverse mode diode lasers as a function of the lasing wavelength. Data are from selected
commercial laser products and research devices. Spectral regimes of relevant material systems
are indicated. Dashed line is guide to the eye.
Two of the key issues, which hampered progress in GaN laser research for a
long time were growth on a poorly lattice-matched substrate (e.g., sapphire) and the
impossibility of realizing p-type conductivity of GaN and AlGaN. By growing on GaN
the lattice mismatch problem has been resolved and it has been shown (Nakamura,
1991) that Mg-doped GaN grown by MOCVD after a suitable post-growth treatment
by annealing turned out to be p-type. Annealing activates the Mg acceptors and yields
a low-resistivity p-type material. AlGaN can be made n- and p-type with Al content
no higher than 30%.
The second striking result is the power of 750 mW ex-fiber at a wavelength of
980 nm (Bookham, Inc., 2009). The technology for this laser device was actually
developed by IBM Laser Enterprise, Zurich, in the early 1990s and comprises a
compressively-strained InGaAs/AlGaAs GRIN-SCH SQW structure grown latticematched on an n-GaAs substrate by MBE. A carefully designed and wet-etched, selfaligned, narrow (∼3–4 μm) ridge waveguide structure enables the laser to operate in
the fundamental spatial mode up to high currents by yielding linear, kink-free light
output powers up to 1.4 W ex-facet (Lichtenstein et al., 2004). The laser has a very
high rollover power of 1.75 W at 25 ◦ C heat sink temperature, and, taking into account
a single-mode near-field pattern of size ∼3 μm × 0.6 μm FWHM, the maximum
power density is well above 100 MW/cm2 without causing any COMD failures.
The proprietary facet passivation technology includes facet cleaving in ultrahigh
vacuum followed by depositing in situ a thin silicon passivation layer with a thickness
10 nm depending on the technique used for depositing the reflectivity modification
coatings outside the high-vacuum chamber. This technique has proven to provide
maximum protection from laser chip failures due to any gradual and sudden facet
degradation mechanisms. The excellent and unique performance and reliability data
of this laser comply fully with the stringent highest requirements established for
42
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
pumping erbium-doped fiber amplifiers (EDFAs) used in terrestrial and submerged
optical communication systems.
We will learn more about this laser type when we discuss in Chapters 2 and 4
design considerations for high-power, single-mode emission and for optical strength
enhancements at laser mirrors, respectively.
1.2.5.2
Standard 100 μm wide aperture single emitters
Table 1.3 lists the best wavelength-dependent optical power values found for 100 μm
wide broad-area (BA) diode lasers in the range 405 to 2200 nm. These devices usually
lase in the fundamental transverse vertical mode (fast axis), but not in the fundamental transverse lateral mode (slow axis). However, there are techniques available to
improve the operation of BA lasers in the fundamental lateral mode, which will be
discussed in Section 2.4. Nevertheless, the data in the table are meant for information
and comparison.
There are two values which catch the eye, the 25.3 W cw at 940 nm (PetrescuPrahova et al., 2008) and 9 W cw at 1240 nm (Bisping et al., 2008).
The former data are for InGaAs/GaAsP QW devices with optimized cavity lengths
L and d/Γ tv ratios aimed at maximizing the thermal rollover power, where d is the
total active region width and Γ tv the transverse vertical optical confinement factor
(see Section 1.3 for basic relations). Crucial to the design is that L directly scales
Table 1.3 State-of-the-art, continuous wave (cw), optical output powers of
broad-area commercial and research diode lasers with 100 μm wide apertures
as function of the lasing wavelength from the blue to mid-infrared regime.
Selected products and research devices (status 2009).
Wavelength
[nm]
Cw power
[W]
Company/institution
405
450
630
690
750
808
915
940
960
975
1060
1210
1240
1300
1500
1850
1900–2200
0.25
0.50
0.40
1.00
1.50
5.00
20.00
25.30
20.00
20.00
16.00
2.00
9.00 (200 μm wide)
8.00
5.00
1.00
2.00
Nichia (2009)
Nichia (2009)
LDX Optronics (2009)
nLight (2009)
LDX Optronics (2009)
Li et al. (2008); Lumics (2009)
Bookham (2009)
Petrescu-Prahova et al. (2008)
Bookham (2009)
Bookham (2009)
Tarasov et al. (2004)
LDX Optronics (2009)
Bisping et al. (2008)
Livshits et al. (2000)
Garbuzov et al. (1996)
LDX Optronics (2009)
Kelemen et al. (2008)
BASIC DIODE LASER ENGINEERING PRINCIPLES
43
proportional to d/Γ tv , that is, higher d/Γ tv ratios can be obtained by lowering Γ tv
and keeping d constant at 6–7.5 nm (cf. also “Broad waveguides” in Section 2.1.3.5).
This has two consequences. First, a low Γ tv reduces the overlap at the output mirror
between the high optical power generated in longer devices and the active QW,
which is vulnerable to degradation. Second, the threshold current density of about
130 A/cm2 is the same for all devices in the optimization process (see Section 1.3).
The thermal rollover power increases with d/Γ tv in the range of 0.78 to 1.17 μm and
L in the range of 3.5 to 5 mm with a record maximum cw power of 25.3 W achieved
for d/Γ tv = 1.17 μm and L = 5 mm. The high d/Γ tv values are obtained by using
an asymmetric structure, which includes an optical trap on the n-side (cf. “Optical
traps” in Section 2.1.3.5 and Chapter 4 for optical strength enhancement techniques).
The optical trap pulls most of the guided optical field to the n-side and reduces Γ tv
to typical values between 0.5 and 0.7%. The devices are mounted on water-cooled
Cu carriers.
The 9 W at 1240 nm in the table is for laser structures based on a
Ga0.68 In0.32 N0.007 As0.993 QW 6.5 nm thick embedded in GaAs0.99 N0.01 strain compensating layers 5 nm thick. This active region is centered in a GaAs SCH layer
1100 nm thick with adjacent Al0.4 Ga0.6 As cladding layers 1200 nm thick. The laser
devices have internal optical losses as low as 0.5 cm−1 , high internal quantum efficiencies of 80%, and excellent temperature dependence of the P/I characteristic
(see Section 1.3 for basic relations). These favorable data, which result from an optimized vertical structure and the high quality of grown materials, have led finally
to the highest room temperature, cw output power ever reported for a high-power
laser in the technologically important wavelength range around 1240 nm. The power
of 9 W has been achieved for a device 200 μm wide and 2.5 mm long. To make
it comparable to standard 100 μm wide devices, the power has to be scaled and a
best-guess value may be around 5 W in the absence of any further information. This
power, however, has to be compared to the 8 W cw obtained from an AR/HR-coated
InGaAsN SQW laser 100 μm wide emitting at a wavelength of 1.3 μm (Livshits
et al., 2000).
1.2.5.3
Tapered amplifier lasers
A selection of the highest optical power levels for tapered amplifier lasers can be
found in Table 1.4. The two high powers of 10 W (Ostendorf et al., 2008) and
12 W (Paschke et al., 2008) are for similar devices comprising InGaAs/AlGaAs
QW vertical structures. Typical lengths for the ridge waveguide oscillator section are
2 mm and for the tapered amplifier section 4 mm. In the latter example with the higher
power, a 1 mm long, sixth-order surface grating defined by projection lithography
and fabricated by reactive ion etching was implemented in the ridge waveguide. This
device shows longitudinal single-mode emission at 980 nm over the full operating
range up to record-high 12 W cw and nearly diffraction-limited optical power at 15
A drive current with a high average slope efficiency of 0.85 W/A and conversion
efficiency of 44% (cf. Section 1.3.7.1 for definitions).
44
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Table 1.4 State-of-the-art, continuous wave (cw), optical output powers
of selected tapered amplifier single-emitter lasers at various lasing
wavelengths. Selected products and research devices (status 2009).
1.2.5.4
Wavelength
[nm]
Cw power
[W]
Company/institution
757
770
787
855
975
976
980
982
1037
1064
1240
1550
0.5
1.0
1.5
0.5
8.3
10.0
12.0
2.0
1.0
4.0
1.0
1.0
m2k/DILAS (2009)
m2k/DILAS (2009)
m2k/DILAS (2009)
m2k/DILAS (2009)
Michel et al. (2008)
Ostendorf et al. (2008)
Paschke et al. (2008)
m2k/DILAS (2009)
m2k/DILAS (2009)
Ostendorf et al. (2009)
Bisping et al. (2008)
QPC (2009)
Standard 1 cm diode laser bar arrays
Table 1.5 shows the highest cw power levels detected for incoherent monolithic diode
laser bar arrays. Optimized material quality and innovative design of the vertical laser
structure, mounting, and cooling techniques led to first output powers beyond the 500
W barrier with 509 W cw at 540 A from 1 cm InGaAs/AlGaAs bars with a 50%
filling factor and 3 mm cavity length. The high power is due to a low-loss waveguide
structure with a low fast-axis, far-field angle of 27◦ , high power conversion efficiency
Table 1.5 State-of-the-art, continuous wave (cw) power levels detected for
incoherent monolithic 1 cm diode laser bar arrays versus lasing wavelength
from the red to mid-infrared regime. Selected products and research devices
(status 2009).
Wavelength
[nm]
Cw power
[W]
638
790
808
825
915
940
8
100
100
100
200
200
940
509
940
980
1030
1870
1900–2200
950
200
110
10
20
Company/institution
Mitsubishi Electric (2009)
nLight (2009)
nLight (2009)
nLight (2009)
Bookham (2009)
Bookham (2009)
Jenoptik Diode Lab (2006);
Sebastian et al. (2007)
Li et al. (2007)
Bookham (2009)
Bookham (2009)
m2k/DILAS (2009)
Kelemen et al. (2008)
BASIC DIODE LASER ENGINEERING PRINCIPLES
45
>68%, optimized facet coatings, and efficient active cooling (Jenoptik Diode Lab,
2006; Sebastian et al., 2007). Significantly improved 980 nm laser bar structures with
low internal loss α i < 0.6 cm−1 , high internal quantum efficiency ηi > 98%, high
T0 ∼
= 200 K, and Tη ∼
= 700 K (see Section 1.3 for definitions of these various
parameters) enable first record-high cw output power of 950 W at 1120 A (supply
limit) from a microchannel-cooled 1 cm bar (Li et al., 2007). The bar consists of 65
emitters, each 115 μm wide and 5 mm long, has a 77% filling factor, and performs
with a conversion efficiency ηc of 70 and 67% for 4 and 5 mm cavity lengths,
respectively. Far-field beam divergence angles for laser bars are typically in the range
of 5 to 10◦ FWHM and 20 to 35◦ FWHM in the slow-axis and fast-axis direction,
respectively, depending on the technology and layout of the bar used.
1.3
1.3.1
Selected relevant basic diode laser characteristics
Threshold gain
Light generated in the active region of the laser device propagates along the optical
waveguide of the active layer structure and is partially reflected at the mirror facets of
the Fabry–Pérot resonator, which contains the laser active material. This propagation
and repeated reflection of light cause a loss and gain of light. Loss is formed by two
components: first, mirror losses, which are caused by the final mirror reflectivities;
and, second, cavity losses, which are due to free-carrier absorption losses in the active
layer and cladding layers as well as scattering losses at structural inhomogeneities of
the heterointerfaces.
Gain is generated in the stimulated emission process, which is turned on by
population-inverted energy levels due to heavy carrier injection. We have to distinguish between material gain, which is the gain of the actual active material, and
modal gain, which is determined by the ratio of the transverse dimension of the
active layer to that of the cavity mode and depends on the details of the specific laser
configuration. Modal gain is always smaller than material gain. This topic will be
described in detail in the following sections.
Figure 1.16 illustrates the loss and gain of power of a propagating optical mode
in a cavity of length L and with mirror reflectivities R1 and R2 . Internal optical losses
of the unbounded active material per unit length are expressed by a loss coefficient α i
in units of cm−1 and volume gain per unit length of the active material is expressed
by the gain coefficient g also in units of cm−1 . Thus, we obtain for the power Prt of
the optical mode after one roundtrip with P0 the power at the start
Pr t = P0 R1 R2 exp{2L (g − αi )}.
(1.22)
The threshold condition states that the gain compensates the loss after one
roundtrip. In this case, Prt = P0 , and we obtain for the threshold gain
gth = αi +
1
ln
2L
1
R1 R2
(1.23)
46
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.16 Schematic illustration of gain and loss of an optical wave during a roundtrip in
a Fabry–Pérot resonator with initial power P0 , cavity length L, internal loss α i , gain g, and
mirror reflectivities R1 and R2 .
which is the minimum gain for turning on the lasing operation. The first term is the
internal cavity loss as described above (see also the next sections). The second term
characterizes the mirror loss α m . Let us take a simple AlGaAs/GaAs laser with a
bulk active layer, cleaved uncoated facets, and a length of 600 μm to illustrate the
magnitude of the threshold gain. The mirror loss is calculated to be ∼
= 20 cm−1 by
∼
using R = 0.32 (see Equation 1.12) and for the internal loss in the bulk active layer
∼
= 15 cm−1 is a typical value which leads in total to a threshold gain of about 35 cm−1
required to start the lasing process.
1.3.2
Material gain spectra
1.3.2.1
Bulk double-heterostructure laser
In Section 1.1.1.2, “Net gain mechanism,” we showed that the lasing operation can
be achieved for the condition EFc − EFv ≥ hν ≥ Eg (see Equation 1.10) involving
photons with energies hν larger than the bandgap energy. A semiconductor meeting
this condition is in the state of population inversion, resulting in Rstim > Rabs or, in
other words, a photon is amplified rather than absorbed. The gain is zero for hν <
Eg , since there are no carrier recombinations at these energies, and it becomes zero
again at hν = EFc − EFv .
The limiting case EFc − EFv = Eg is called the transparency condition, where
the gain is zero for a photon energy hν = Eg . A typical minimum carrier density
to achieve transparency in a bulk GaAs/AlGaAs laser is Ntr ∼
= 1.5 × 1018 cm−3 .
At transparency, the material losses of the active material are compensated by the
optical gain. The transparency density includes both radiative carrier loss such as
spontaneous recombinations and nonradiative carrier loss including carrier escape.
When the density of injected carriers N is larger than the transparency density,
then EFc − EFv > Eg and a net gain develops for photon energies between Eg and
EFc − EFv .
BASIC DIODE LASER ENGINEERING PRINCIPLES
47
Figure 1.17 Schematics of the gain formation for various carrier densities N injected in a bulk
DH laser. The material is transparent for photon energies smaller than the bandgap energy Eg
of the semiconductor material. The inset shows the typical linear dependence of the maximum
gain gmax on carrier density N for a bulk laser (3D). Ntr is the carrier density at transparency.
Typical plots of optical gain (or loss = negative gain) spectra as a function
of photon energy are illustrated schematically in Figure 1.17 at different injection
currents (carrier densities). Quantitative, calculated gain spectra can be found in
various textbooks (e.g. Yariv, 1997).
One can observe two key features. First, with increasing carrier density, the difference in quasi-Fermi energies EFc − EFv increases, and this results in a broadening
of the spectra or increase in the gain bandwidth. The bandwidth increase is, however,
small and was evaluated to about 3% of the bandgap energy at a carrier injection
of 2.5 × 1018 cm−3 . Second, the gain peak shifts gradually to higher energies due to
band-filling effects. At higher photon energies, the semiconductor absorbs.
The remarkably simplifying feature is that for typical gain coefficients of interest
in a bulk DH laser (20 < g < 80 cm−1 ), the variation of the volume material gain
curve maximum versus the density of injected carriers can be well approximated by
the linear relation
gmax = g = σ (N − Ntr )
(1.24)
where σ = dg/dN is the differential gain with the dimension of an area. Typical values
for σ are 1.5 × 10−16 cm2 and 1 × 10−16 cm2 for GaAs and In0.58 Ga0.42 As0.9 P0.1 ,
respectively (Yariv, 1997; Svelto, 1998).
1.3.2.2
Quantum well laser
Schematic material gain spectra for a QW laser at different injection currents are
illustrated in Figure 1.18.
There are several interesting characteristics. Due to the high density of states and
its narrow energetic distribution, the maximum of the gain curve shows nearly no
48
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.18 Material gain spectra g(E) of a single quantum well laser are illustrated schematically as a function of injected carrier density N. The inset shows a larger initial slope of the
maximum gain gmax versus N dependence than in 3D due to the much higher density of states in
a quantum well (2D); however, gmax saturates when electron and hole states are fully inverted.
Ntr is the carrier density at transparency. At higher carrier injections, the population of the next
higher n = 2 quantized state contributes to the gain.
shift in energy with increasing current. For the same reasons the material gain is
also higher than in bulk DH lasers according to calculations (Yariv, 1997). The same
calculations showed also that equal increments of current will yield larger increments
of gain in QWs, and that the energetic spread for effective gain is larger by a factor
of about 2–3 than in DH lasers.
Due to the two-dimensional density of states in QWs, carriers are more efficient
than in a bulk laser, because added carriers contribute to the gain at its maximum.
In contrast to DH lasers, carriers move the gain peak away from the bottom of the
band, rendering all carriers at energies below that of gmax as useless (compare insets
in Figure 1.17 and Figure 1.18). For the same reason the differential gain is higher
at lower injection levels than in the bulk. However, the gain saturates at an injection
when the electron and hole states are fully inverted, whereas the maximum never
saturates in a bulk DH laser due to the filling of an ever-increasing density of states.
Also Ntr (QW) Ntr (bulk DH) because the density of states to be inverted is
significantly smaller; for example, a GaAs QW has ≈1012 states/cm2 in the minimal
energy range of kB T to be inverted, compared to ≈1013 states/cm2 in an active layer
of a DH laser 100 nm thick (Weisbuch and Vinter, 1991).
A final interesting feature in Figure 1.18 is that the gain peak at the lower energy,
which is due to the population of the n = 1 well ground state, flattens with increasing
current and a second peak appears at higher currents due to the population of the next
higher n = 2 state.
For QW lasers, the gain and injection carrier density relation is nonlinear, because
the gain saturates in a g versus N plot at sufficiently high carrier injections due to the
flat feature of the two-dimensional, step-like density of states (Zhao and Yariv, 1999;
BASIC DIODE LASER ENGINEERING PRINCIPLES
49
Coldren and Corzine, 1995). We can approximate the material gain versus carrier
injection density relation for a SQW laser by
g = g0 ln
N
Ntr
(1.25)
where g0 is the gain constant (which is proportional to the differential gain) for one
QW. Equation (1.25) can be extended to a MQW laser by adding the factor nqw for
the number of QWs. For not very large nqw values, the QWs are decoupled and the
carrier injection is uniform within the QWs. Then the modal gain gmod , which is the
material gain g multiplied by the confinement factor Γ , which we will see in the next
sections, is approximately proportional to nqw because each QW contributes almost
equally to the laser mode field.
1.3.3
Optical confinement
The optical confinement factor Γ plays a key role in the design of any semiconductor
diode laser. It is defined as the degree of overlap of the optically guided wave with
the gain region of thickness d and can be written as
Γ = Γtv =
+d/2
−d/2
+∞
−∞
|E(z)|2
dz
|E(z)|
(1.26)
2
where |E(z)2 | is the electric field intensity profile in the direction z perpendicular to
the active layer. This is the definition of the transverse vertical confinement factor
Γtv ; a similar expression to Equation (1.26) can be defined for the transverse lateral
confinement factor Γtl with the integration then over the width w of the lateral
waveguide. A simplified illustration for the transverse vertical confinement factor
can be found in Figure 1.19.
In general, thin active layers lead to a broad spreading of the optical mode resulting
in a large near-field spot size, which transforms into a narrow far-field divergence
angle. In contrast, thick active layers give a narrow, well-confined mode with a small
near-field spot size and consequently a large far-field angle. This information is used
to optimize the performance of QW lasers, tune the laser beam divergence angles,
and maximize the optical strength of the mirror facets at high optical power outputs.
These aspects will be discussed in the sections and chapters that follow.
For the fundamental transverse vertical mode, Botez (1978, 1981) derived a
remarkably simple expression accurate to within 1.5%
Γtv ∼
=
D2
(2 + D 2 )
(1.27)
50
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.19 A simplified illustration of the transverse vertical optical confinement factor Γtv .
|E(z)|2 is the electric field intensity profile in the direction z perpendicular to the active layer,
nr,cl and nr,a are the refractive indices of the cladding layers and active layer, respectively.
with
D = 2π
d 2
n − n 2r,cl
l r,a
1/2
(1.28)
where nr,a and nr,cl are the refractive indices of the active layer and the claddings,
respectively, and l is the lasing wavelength. The effective index was also derived
(Botez, 1981) and can be approximated by
2
n 2r,eff ∼
− n 2r,cl .
= n 2r,cl + Γtv n r,a
(1.29)
This will be required for the discussion on the lateral modes in the next chapter.
To achieve a large modal gain
gmod = Γtv g
(1.30)
the normalized thickness D of the active layer has to be large. However, as we will
see in the discussion on the single spatial mode in the next chapter, this will lead
to the excitation of higher order modes and, in order to let the laser operate in the
fundamental vertical mode, D has to be below a critical value. Similar expressions to
Equations (1.27) to (1.29) can be written for the lateral confinement issue. These will
be defined and used in Chapter 2 also for establishing the conditions for fundamental
lateral mode operation.
Figure 1.20a shows the dependence of Γtv on the active layer thickness d calculated for a 980 nm In0.2 Ga0.8 As/Al0.3 Ga0.7 As DH laser. Typical values are 25% for
an active layer 100 nm thick; however, for a 10 nm QW confinement factors are as
low as a few percent. The confinement factor for a SCH SQW laser with thickness
Lz can be evaluated by
Γtv,qw ≈
Lz
dmode
(1.31)
BASIC DIODE LASER ENGINEERING PRINCIPLES
51
Figure 1.20 (a) Transverse vertical optical confinement factor Γ tv calculated as a function
of the active layer thickness d of a 980 nm In0.2 Ga0.8 As/Al0.3 Ga0.7 As DH laser by using for
the refractive indices nr (Al0.3 Ga0.7 As) = 3.3 and nr (In0.2 Ga0.8 As) = 3.7. (b) Calculated Γ tv
as a function of the GRIN-SCH layer thickness and AlAs x mole fraction in the Alx Ga1–x As
cladding layers of In0.2 Ga0.8 As/Alx Ga1–x As 6 nm SQW lasers. High Γ tv values are in the upper
right corner and low values in the lower left corner of the greyscale contrast image.
where dmode is the spread of the mode perpendicular to the active layer, which
is roughly the thickness of the SCH layer. Detailed calculations (Nagarajan and
Bowers, 1999) yielded confinement factors of typically 3% for a 5 nm InGaAs SQW
embedded in different AlGaAs SCH energy profiles including step-SCH and GRINSCH structures.
Figure 1.20b shows transverse vertical confinement factors calculated as a function of the AlGaAs GRIN-SCH layer thickness and AlAs x mole fraction in the
Alx Ga1−x As cladding layers of In0.2 Ga0.8 As/Alx Ga1−x As 6 nm SQW lasers. For the
calculation we used the LASTIP simulation code (Crosslight Software Inc., 2010)
already introduced in Section 1.1.4 above. High confinement factors above 2% can be
found in the greyscale contrast image in the upper right corner and low confinement
factors around 1% in the lower left corner. The data can be understood in terms of
52
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.21 Simplified schematics of gain and loss in the individual vertical layers of a
Fabry–Pérot cavity structure with the end mirror reflectivities R1 and R2 .
high AlAs x values (low refractive index) leading to stronger mode confinement and
therefore higher Γ tv values dependent on the GRIN-SCH thickness, whereas low
GRIN-SCH thicknesses and low AlAs x values (high index) lead to strong mode
spreading and hence to low confinement factors (see also “Thin waveguides” in
Section 2.1.3.5).
1.3.4
Threshold current
To derive an expression for the threshold current requires knowledge of the modal
gain at threshold and combining it with the relevant modal gain versus injection
carrier density relation. The optical field distribution in the laser structure has to be
considered, which includes the distribution of gain and loss in the individual layers
as given by the confinement factor Γ tv . This is illustrated for a simple Fabry–Pérot
structure in Figure 1.21.
In the following sections, we will derive the threshold current for a DH and QW
laser and discuss the variation of threshold current with active layer thickness and
cavity length.
1.3.4.1
Double-heterostructure laser
From Equations (1.22) and (1.23) we obtain
Γtv gth = Γtv αa + (1 − Γtv ) αcl +
1
1
ln
2L
R1 R2
(1.32a)
or
gth = αa +
(1 − Γtv )
1
1
ln
αcl +
Γtv
2Γtv L
R1 R2
(1.32b)
where α a and α cl denotes the loss in the active layer and cladding layers, and Γ tv gth
is the modal gain or amplification of the optical wave per unit length at threshold.
Γ tv α a is the loss per unit length of the guided wave in the active layer. Therefore,
(1 – Γ tv )α cl is the loss of the optical mode per unit length outside of the active layer
in the confining material. Equation (1.32) simply states that the modal gain is exactly
BASIC DIODE LASER ENGINEERING PRINCIPLES
53
balanced by the total losses including active layer, cladding layer and mirror losses.
Using Equation (1.24) we obtain for the threshold carrier density Nth
Nth =
1 − Γtv
αa
1
1
+
αcl +
ln
+ Ntr .
σ
σ Γtv
2Lσ Γtv R1 R2
(1.33)
The threshold current density Jth is related to the threshold carrier density Nth by
Jth =
qd
Nth
ηi τr
(1.34)
where ηi is the internal quantum efficiency, which is the fraction of carriers that
recombine radiatively (see one of the next sections), τ r is the radiative recombination time, q the electron charge and d the active layer thickness. Equation (1.34)
was obtained from R = ηi Jth /qd for the recombination rate of carriers injected
with current density Jth and from the steady state condition for the carrier density
Nth = Rτ r . Finally, we obtain the desired expression for the current density at lasing
threshold as
Jth =
qd
ηi τr
αa
1 − Γtv
1
1
+
αcl +
ln
+ Ntr .
σ
σ Γtv
2Lσ Γtv R1 R2
(1.35)
An example may demonstrate the usefulness of these equations. We take an
AlGaAs/GaAs DH laser with uncoated facets (R1 = R2 ∼
= 0.32), refractive indices
nr,a = 3.6, nr,cl = 3.4, an active layer thickness of d = 0.1 μm, a cavity length of L =
300 μm, and a lasing wavelength of 850 nm. For simplicity reasons, we assume α a =
α cl = α i and take 10 cm−1 as a typical value for the loss coefficient in an AlGaAs/GaAs
DH laser. The confinement factor is then calculated as Γ tv ∼
= 0.25 by using Equations
(1.27) and (1.28). Finally, by taking 3.6 × 10−16 cm2 for the differential gain σ and
2 × 1018 carriers/cm3 for the transparency density Ntr (Svelto, 1998), we obtain for
the threshold carrier density Nth = (0.11 + 0.42 + 2) × 1018 carriers/cm3 . To evaluate
the threshold current density, we take ηi ∼
= 0.9 and τ r ∼
= 4 ns as typical values and
−16
∼
A cm) × (2.53 × 1018 carriers/cm3 ) = 1125 A/cm2 . This
obtain Jth = (4.45 × 10
calculated value is in remarkably good agreement with experimental values.
If the mirror losses are much greater than the internal losses, the threshold current
density dependence expressed in Equation (1.35) is then mainly determined by the
ratio d/Γ tv , which has an optimum value for a normalized thickness D = 1.42
(cf. Equations 1.27 and 1.28).
As can be seen from Equation (1.35), the transparency current Jtr can be determined from measurements on lasers of different cavity lengths L and by plotting Jth versus 1/L. The intersection of the plot with the Jth axis yields Jth,1/L=0 =
Jtr + (qdα i )/(ηi τ r Γ tv σ ) by again using α a = α cl = α i , that is, not splitting the intrinsic
loss into losses in the active and passive regions of the optical waveguide for simplicity reasons. Jtr can be extracted from the intersection point value by subtracting the
54
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
second term, which requires knowledge of the values of the individual parameters α i ,
ηi , τ r , Γ tv , σ . The dependence of the threshold current on cavity length and active
region thickness will be discussed in Sections 1.3.4.3 and 1.3.4.4, below.
1.3.4.2
Quantum well laser
A procedure similar to that described in Section 1.3.4.1 can be applied to a QW laser
by rewriting Equation (1.32b) as
1 − n qw Γtv,qw
1
1
ln
gth = αa +
αcl +
(1.36)
n qw Γtv,qw
2n qw Γtv,qw L
R1 R2
where nqw is the number of QWs in the active region and Γ tv,qw is the transverse
vertical optical confinement factor of one QW.
The threshold carrier density is then obtained with the help of Equation (1.25) as
1
1
/ n qw Γtv,qw g0 .
Nth = Ntr exp n qw Γtv,qw αa + 1 − n qw Γtv,qw αcl +
ln
2L
R1 R2
(1.37)
We select as an example an AlGaAs/GaAs SQW (nqw = 1) laser with similar
parameters and simplifications as in the above DH laser, but with a well thickness
Lz = 10 nm, a confinement factor Γ tv,qw = 0.03, a gain constant g0 ∼
= 2400 cm−1
18
−3
∼
and a transparency density Ntr = 2.5 × 10 cm (Coldren and Corzine, 1995).
Equation (1.37) then yields Nth ∼
= 2 × Ntr ∼
= 5 × 1018 carriers/cm3 . With this value
and Equation (1.34) where d is the well thickness Lz , the threshold current density
becomes Jth ∼
= 220 A/cm2 , which is
= (4.5 × 10−17 A cm) × (5 × 1018 carriers/cm3 ) ∼
in good agreement with experimental values.
1.3.4.3
Cavity length dependence
We take a QW laser for the discussion and rewrite Equation (1.37) as the current at
lasing threshold
1
1
ln
Ith = wLJ tr exp αi +
/ n qw Γtv,qw g0 .
(1.38)
2L
R1 R2
Here w is the active layer width, L is the laser length, and Jtr = (qLz /ηi τ r )Ntr is
the transparency current, which was obtained from Equation (1.34) for the relation
between current density and carrier density. For simplicity, we do not distinguish
between active and passive losses and again set α a = α cl = α i . The threshold current
dependence on cavity length of a QW laser is different from that of a bulk DH laser.
It can be shown from Equation (1.38) that there is a minimum threshold current for
a QW laser at
1
1
wJ tr
αi
+1
(1.39)
×
× exp
Ith,min = ln
2 R1 R2
n qw Γtv,qw g0
n qw Γtv,qw g0
BASIC DIODE LASER ENGINEERING PRINCIPLES
55
which is achieved at a length
L min =
1
1
1
×
.
ln
2 R1 R2
n qw Γtv,qw g0
(1.40)
From the last three equations, we can evaluate how the number of QWs determines
the threshold current. Both the transparency current and internal loss coefficient consist of a part, which scales with the number of QWs and a part, which is independent
of it. For the transparency current, the radiative loss of carriers within the active
QW is proportional to the number of QWs. In contrast, the carrier loss in the SCH
region, which embeds the QW, and the carrier leakage are actually independent of the
number of QWs. The internal loss coefficient consists of free-carrier absorption in
the active QW, which scales with the number of QWs. It also consists of free-carrier
absorption in the region adjacent to the QW, waveguide scattering, and impurity absorption effects, all of them are independent of the number of QWs. There is also a
strong influence on the threshold current versus number of QWs dependence by the
threshold modal gain. At low modal gain, the exponential term in Equation (1.38)
tends to one, with the consequence that the threshold current of SQW lasers becomes
lower due to a lowering of the transparency current density. At high threshold modal
gain, the exponential term in Equation (1.38) dominates the threshold current. The
use of MQWs will significantly reduce this term leading together with a higher gain
coefficient to lower threshold currents despite the fact that the transparency current
density is larger than in SQW lasers. We can see from Equations (1.39) and (1.40)
that lower minimum threshold currents can be obtained at shorter laser lengths in
MQW lasers (Zhao and Yariv, 1999).
Using the data of the example discussed in the last part of Section 1.3.4.2 we can
get for a laser with a width of 4 μm and length 300 μm a threshold current of about
3 mA. In addition, from Equations (1.39) and (1.40) the threshold current minimum
becomes about 2 mA at a cavity length of 160 μm for a SQW laser 4 μm wide with
the same data as used in the example in the last section. These results are in excellent
agreement with experimental data (Chen et al., 1992).
Figure 1.22 shows schematically the cavity length dependence of the threshold
current of a QW laser. There are typically three different ranges. The linear curve for
lengths L > Lmin represents the fact that the threshold current increases with cavity
length. In that regime the slope of the curve increases with the number nqw of QWs
and also increases with the interface recombination velocity vs , which is a measure
for the loss of carriers due to nonradiative recombination via defect states in the
bandgap of the active QW.
The regime around the minimum is characterized by a threshold, which decreases
with nqw , increases with vs , and decreases with mirror reflectivity R1 , R2 at a cavity
length Lmin decreasing with increasing nqw and R1 , R2 (Engelmann et al., 1993). A
high reflectivity, however, leads to a low external differential quantum efficiency, as
we will see in one of the sections below, because it is basically the ratio between
mirror loss and total cavity loss.
56
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.22 Schematic illustration of the cavity length dependence of the threshold current
of a quantum well laser characterized by three different ranges: (i) threshold Ith,min and cavity
length Lmin at the minimum, (ii) strong increase of the threshold below the minimum, (iii)
weaker increase of threshold with a certain slope for longer cavities above the minimum.
Dependence ( denotes a decrease, denotes an increase) of Ith,min , Lmin , and slope on
increasing number of quantum wells nqw , interface/surface recombination velocity vs , and
reflectivities R1 , R2 is indicated.
In the regime L < Lmin the threshold current shows a striking increase toward
short cavity lengths, which is a direct consequence of the gain saturation in a QW
laser at high carrier injections and the dominating mirror losses (see Equation 1.38).
A large gain is required to overcome the high mirror losses in this short-cavity effect
regime. According to Engelmann et al. (1993), this anomalous increase of Ith shifts to
smaller L values with increasing nqw , which multiplies the fraction of the optical mode
subject to the gain due to an increased Γ tv and therefore suppresses the gain saturation
problem even at very short cavities. The short-cavity effect is particularly pronounced
in SQW lasers due to a low gain confinement Γ tv . Its location is affected by Auger
recombination and carrier leakage but to a lesser extent by interface recombination.
1.3.4.4
Active layer thickness dependence
The variation of the threshold current density Jth with active layer thickness d is
plotted in Figure 1.23 for an AlGaAs/GaAs DH and a GRIN-SCH SQW laser. In the
case of the DH laser, we can understand and analyze the dependence with the help
of Equation (1.35).
For sufficiently large values of d above the minimum, the threshold carrier density
Nth is nearly the same as the transparency density Ntr , as can be seen from the example
in Section 1.3.4.1, and Ntr increases with d like the number of states to be inverted.
The differential gain σ decreases because fewer states per unit volume are populated
by the same drive current density and the slight increase of the confinement factor
BASIC DIODE LASER ENGINEERING PRINCIPLES
57
Figure 1.23 Experimental variation of the threshold current density Jth with active layer
thickness d plotted for an AlGaAs/GaAs DH and a GRIN-SCH SQW (inset) laser. Small
current steps at wider quantum well widths indicate the population of higher subbands.
Γ tv can be considered as negligible. Therefore, considering all effects, Jth increases
linearly with d in the region of larger active layer thicknesses.
However, for sufficiently small d values the 1/Γ tv terms in Equation (1.35) increase dramatically because: (i) the confinement factor Γ tv diminishes very quickly
in proportion to d2 (see Equations 1.27 and 1.28); (ii) the mode extends considerably into the doped cladding layers; (iii) the transparency density decreases only
proportional to d; and (iv) the differential gain increases only in proportion to 1/d.
Overall, including a reduced effective gain and increased losses leads to a strongly
increased threshold carrier density resulting in a dramatic increase in the threshold
current density as the active layer thickness decreases to small values.
In the case of the GRIN-SCH SQW laser, we use the results of detailed calculations
carried out on the volume gain versus injection current dependence with the well
thickness as parameter (Weisbuch and Vinter, 1991).
These calculations showed a continuous decrease in the transparency current
with decreasing well thickness from high, quasi-3D values to smaller values and an
increase in the volume gain with diminishing d as the volume diminishes. The confinement factor decreases proportional to d with decreasing d (see Equation 1.31). Using
Equations (1.34) and (1.37) we conclude therefore that the transparency current is the
main parameter responsible for the decrease in the threshold current density with decreasing d in the region of larger d values (see inset of Figure 1.23). In this regime, the
population of higher lying quantum states may also play a role, in particular for wider
wells, as the subband spacing becomes smaller. This is indicated by the appearance
of small current steps in the Jth versus d plot shown in the inset of Figure 1.23.
In very thin wells carriers escape into the GRIN-SCH optical confinement region
leading to a large transparency current, which is the main source for the strongly
increasing threshold current density in very thin well layer lasers. The carrier escape
is caused by the large confining energy, which drives the quasi-Fermi level high in the
58
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
well. The effects at both larger and smaller well thicknesses account for the existence
of a minimum in the Jth versus d dependence.
1.3.5
Transverse vertical and transverse lateral modes
The distribution of the propagating optical fields in the laser cavity can generally
be characterized by two independent sets of modes, transverse electric (TE) and
transverse magnetic (TM) ones. As already discussed above, these are subdivided into
transverse vertical modes, which are perpendicular to the active layer, and transverse
lateral modes, which are parallel to the active layer. TE modes have polarizations with
the electrical field vector parallel to the active layer as opposed to TM modes where
the light is polarized perpendicular to the active layer. Semiconductor diode lasers
usually operate in the TE mode due to the lower threshold gain gth (TE) < gth (TM),
which is also true for the technologically important, pseudomorphic, compressively
strained InGaAs/AlGaAs QW lasers (Coleman, 1993).
The transverse vertical mode is formed by the standing wave between the heterojunctions of the active layer structure, which determines the confinement strength
of the optical field, and the conditions for fundamental transverse vertical mode
operation. The latter will be discussed in detail in Chapter 2, whereas the optical
confinement issue was briefly discussed in Sections 1.1.1.4 and 1.3.3. The following
section gives a rundown of possible vertical confinement structures along with their
key features.
The transverse lateral mode is determined by the standing wave in the direction
parallel to the active layer. Fundamental mode operation is strongly determined by the
effective, lateral width and structure of the active region and the change of refractive
index from the active region to adjacent layers. Structures for stabilizing the transverse
lateral mode have already been briefly dealt with in Section 1.1.1.5. Sections 1.3.5.2
and 2.1.4 will discuss this topic in more detail.
1.3.5.1
Vertical confinement structures – summary
Double-heterostructure
r Example: n-AlGaAs/GaAs/p-AlGaAs. dGaAs ≈ 0.08–0.2 μm.
r Efficient carrier confinement due to band discontinuities.
r Optical confinement factor Γ tv large ≈ 0.6 (0.9) at d = 0.2 (0.6) μm.
r Threshold current density large, typically 1 kA/cm2 .
Single quantum well
r Well thickness Lz typically in range of 5 to 10 nm.
r Lasing wavelength adjustable by changing Lz and/or barrier height.
r Γtv,qw ∝ nr L 2 is very low. Example: Γ tv,qw 1% for an InGaAsP/InP SQW
z
with Lz = 10 nm.
BASIC DIODE LASER ENGINEERING PRINCIPLES
59
r Without the optical confinement structure, threshold current density is high
caused by high losses due to spreading of the mode into the lossy cladding
layers and gain saturation at high carrier densities due to the constant density
of states of the n = 1 subband. This makes the threshold current more sensitive
to increased cladding losses, increasing with temperature because of higher
free-carrier absorption at high temperatures.
Strained quantum well
r Lattice-mismatch between well and barrier. Generated strain is elastically relaxed by deformation of the well material if Lz < Lz,crit .
r Access to certain wavelengths not available from any lattice-matched III–V
compound semiconductor system. Example: ∼900–1100 nm band wavelengths only accessible by pseudomorphic, compressively-strained InGaAs/
AlGaAs QW lasers.
r Threshold current density is reduced and slope efficiency of power output
versus drive current characteristic is increased by a reduced density of states
and thus of the reduced hole effective mass due to a strain-induced separation
of light-hole and heavy-hole valence bands.
r Temperature dependence of lasing characteristics is improved with higher
characteristic temperatures.
r High mode selectivity: TE polarized light emission for electron to heavyhole recombinations for compressive strain as opposed to TM polarized light
emission for electron to light-hole recombinations for tensile strain.
Separate confinement heterostructure SCH and graded-index SCH (GRIN-SCH)
r To improve significantly photon and carrier confinement of SQW.
r To counteract carrier overflow from well under high injection.
r To fully exploit reduced density of states in QWs to achieve lasing at low
carrier injection.
r Optimum SCH or GRIN-SCH thickness (waveguide layer) for a given composition difference between cladding layer and waveguide layer is that, which
maximizes the QW optical confinement factor Γtv,qw ∝ n r L 2z . Example:
dSCH ∼
= 170 nm and dGRIN-SCH ∼
= 300 nm for a maximum Γ tv,qw ∼
= 3.5%
for SQW (Lz = 10 nm) AlGaInP/GaInP lasers emitting in the 650 nm band.
Multiple quantum well (MQW)
r Low threshold current densities due to strong optical confinement.
r At high loss: MQW is always better than SQW due to the higher differential
gain in the gain–current curve. In contrast, the saturated gain of the SQW is
not large enough to reach threshold gain.
60
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.24 Schematic illustration of band structure (conduction band only shown for clarity) of various active region structures including DH, SQW, GRIN-SCH, and MQW and
corresponding energy (E) dependent density of states (DOS) for some of them.
r At low loss: SQW is always better than MQW due to both its lower Jtr (only
states of one QW have to be inverted) and lower internal loss (Γ tv,qw α i scales
with number of wells)
Figure 1.24 shows the schematics of the various active layer structures along with
some associated density of states (DOS).
1.3.5.2
Lateral confinement structures
As mentioned in Section 1.1.1.5, transverse lateral confinement has to be realized for
current, carriers, and photons to achieve high performance of edge-emitting diode
lasers. There are practically three types of implementation approaches: gain guiding
provides current confinement, weak index-guiding current, and photon confinement,
and strong index guiding provides current, carrier, and photon confinement. In the
following we describe the concept and key features of each of the approaches.
Gain-guiding concept and key features
As illustrated in Figure 1.25, gain guiding is generated by injecting current through
an aperture in a dielectric insulating layer. Other techniques include the formation
of a current path by Zn diffusion or by restricting the current flow to an opening in
high-resistivity areas created by ion implantation (see also Figure 1.6). The active
region of all these structures is planar and continuous. The optical mode distribution
BASIC DIODE LASER ENGINEERING PRINCIPLES
61
Figure 1.25 Schematic cross-section of a simple gain-guided laser structure with an oxide
stripe for current confinement. The gain-guiding concept is shown for a GaAs/AlGaAs laser.
The effective profiles for carrier density N, gain g, and refractive index nr at high injection
conditions are also shown qualitatively. Layer thicknesses not to scale.
along the active layer is determined by the optical gain and therefore these lasers are
called gain-guided lasers.
Light amplification by stimulated emission occurs only in the gain region, which
is pumped by the injection of carriers through the drive current. Outside this region
high optical losses impact the mode. The optical gain is determined by the carrier
distribution, which is impacted by lateral current spreading in the p-type cladding
layer and carrier diffusion in the active layer. Spatial hole burning (holes burned
in the spatial distribution of inversion within the active region) can occur under
relatively high injection conditions in the center part where the high stimulated
emission rate decreases the carrier density, which leads to an increase in the refractive
index resulting in a contraction of the emission spot width, called self-focusing
(Van der Ziel, 1981). The effective index reduction can be as strong as 5 × 10−3 .
The location of this transverse lateral mode with a highly contracted emission
spot is, however, not stable and can move laterally to higher refractive index areas by
any irregularity in the built-in index profile. This is usually associated with a local
nonlinearity (kink) appearing in the P/I characteristic, because of the spatial separation
of the light confinement region and high-gain region leading to a movement of the
mode along the active layer plane, an excitation of higher order lateral modes or a
transition from the TE to TM mode. Index guiding along the active layer can mitigate
the self-focusing effect by stabilizing the optical mode (Lang, 1980). Fundamental
lateral mode operation can be achieved with narrow-stripe lasers exhibiting kinks at
much higher operating powers than do lasers with wider stripes (waveguides). This
operating mode is necessary for fiber-coupled applications.
Other disadvantages include high threshold current densities and low differential
quantum efficiencies due to lossy waveguides and carrier-induced index suppression resulting in index anti-guiding. Significant astigmatism in the output beam and
high susceptibility to self-pulsations are further undesirable features. Astigmatism
62
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
is caused by the difference in the beam waist position in the direction parallel and
perpendicular to the active layer. In the former, the phase front of the mode is curved
since the mode leaks laterally into an absorbing medium where no current is injected, which locates the beam waist within the cavity; in the latter, the phase front
is plane because of the index guiding locating the beam waist at the mirror surface.
Self-pulsations are sustained oscillations where the emitted light pulsates at high
frequencies of several hundred megahertz. A saturable absorption model can account
for the pulsation phenomenon (Dixon and Joyce, 1979). Central to this model is a
nonlinear gain versus carrier density dependence, which causes regions with smaller
carrier density to act as saturable absorbers.
Weakly index-guiding concept and key features
A possible realization of a weakly index-guided structure was shown in Figure 1.6.
Common to all such designs is that the thickness of at least one layer is laterally
nonuniform. There are many possible structures, which can simply be grouped in rib
and ridge waveguide-type lasers.
In both types of scheme, the lateral laser structure is modified such that an effective
index step of 10−2 is generated in the rib or ridge zone, which is larger than the
carrier-induced index suppression leading then to a relatively stable index guiding
of the lateral mode. In rib lasers the thickness, for example, of the waveguide layer
or the active layer (Figure 1.6), can be varied laterally; however, current spreading
in the p-cladding layer can impact the threshold current density.
In ridge lasers (Figure 1.26) where the ridge is formed in the upper p-cladding
by etching and embedded in a dielectric layer, the loss of effective current by current
spreading is less pronounced. However, carrier diffusion in the active layer, which
extends beyond the ridge impacts the threshold current but also produces a continuous
lateral variation of gain and index. The partial overlap of the mode with the dielectric
layer forms an effective index step with a height determined by the height of the
ridge and the residual thickness to the active layer. A sensitive adjustment of the etch
depth is required to provide enough effective lateral index step for single lateral mode
operation. The beam quality and fundamental mode operation of ridge waveguide
lasers are sensitively dependent on the design of critical ridge dimensions and their
control during device fabrication.
Figure 1.26 Schematic cross-section of a weakly index-guided ridge waveguide laser providing lateral current and photon confinement illustrated for a GaAs/AlGaAs laser. Layer
thicknesses not to scale.
BASIC DIODE LASER ENGINEERING PRINCIPLES
63
This topic will form one of the main discussion points in Chapter 2. Narrow ridge
waveguide, single-emitter lasers have been extensively investigated and are widely
employed in many key application areas because of:
r simple fabrication technology requiring only one single epitaxial growth step;
r low optical losses;
r low threshold currents;
r long lifetimes;
r easy integration; and, above all,
r record-high optical powers emitted in a single transverse vertical and lateral
mode.
Strongly index-guiding concept and key features
The basic structure of a strongly index-guided laser combining all three lateral confinements for current, carriers, and photons was described in Section 1.1.1.5 and
illustrated in its simplest form in Figure 1.6. The active layer is buried on all sides in
higher bandgap materials with lower refractive indices creating a high lateral index
step along the active layer of about 0.3 for InGaAsP/InP, which is at least higher by
a factor of 100 than the index change induced by carriers. Current path and optical
confinement are tightly kept within bounds including lateral carrier diffusion in these
devices, called buried-heterostructure (BH) lasers, resulting in lasing characteristics
determined mainly by the waveguide, which confines the optical mode within the
buried active area. BH lasers come in many different forms, which can be classified
in two groups comprising structures with planar and nonplanar active layers.
We restrict our discussion to a planar-type device, shown in Figure 1.27. It is an
etched mesa BH device, which is fabricated by first growing a planar active waveguide
configuration followed by etching a narrow mesa stripe down to the active layer and
Figure 1.27 Schematic cross-section of an etched-mesa buried heterostructure providing
current, carrier, and photon confinement shown for an InGaAsP/InP laser. The current leakage
path through the mesa burying layers formed by regrowth is indicated in a simplified manner.
Layer thicknesses not to scale.
64
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
subsequently regrowing additional lattice-matched layers with higher bandgap and
lower index to embed this mesa. The purpose of the regrown material is twofold: to
confine current, carriers, and photons to the center part; and to block current flow
in these burying layers. This can be accomplished by reverse-biased homojunctions
under forward-bias operation, whereas the heterojunctions in the center path are
forward biased to inject the confined current into the active layer. Alternatively, highly
resistive material or semi-insulating material such as Fe-doped InP for InGaAsP/InP
lasers can also be used as current blocking layers.
Leakage current Ileak poses a potential issue in BH lasers. Its magnitude varies with
the drive current Ia through the active layer and depends sensitively on the thickness
and carrier concentration of the current-confining layers. The leakage current paths
in a mesa etched BH laser (Figure 1.27) can be summarized as follows (Agrawal and
Dutta, 1993):
r Diode leakage path: Formed by forward-biased homojunction p-InP blocking
layer/n-InP buffer layer. The effective saturation parameter of this diode is
determined by current spreading in the p-InP layer, which is smaller for thinner
p-InP and consequently diode leakage tends to be lower for thin p-InP regrown
layers.
r Transistor leakage path: Formed by n-InP buffer layer (emitter), p-InP blocking
layer (base), and n-InP top regrown layer (collector). Increasing the width of
the p-InP layer increases the base width of the transistor, which reduces the
current gain of the transistor and hence the leakage through the transistor path.
r Thyristor leakage path: Formed by p-InP cladding, n-InP top regrown layer,
p-InP blocking layer, and n-InP buffer layer. The thyristor is off at low currents
and hence leakage through this path is low. At high currents the thyristor may
turn on, leading to very high leakage currents.
BH diode lasers are characterized by positive and negative features. The former
generally include low threshold currents in the range of 10 to 20 mA, bandwidths
as high as 22 GHz have been demonstrated in 1.3 μm lasers with low-capacitance
structures (Huang et al., 1992), and operation to high output powers in stable, fundamental mode operation for active layer widths of 1.5 μm in the 1.55 μm band of
InGaAsP/InP communications lasers. The latter include complex fabrication technology steps, relatively high threshold current densities, and the degradation of the
buried heterointerface as a potential, additional degradation mechanism. This mode
is associated with a breakdown or degradation of the active region due to a decrease
of injected carriers. The degradation of the buried heterointerface can be classed as a
wear-out failure and not a sudden failure (see Chapters 3 and 5).
1.3.5.3
Near-field and far-field pattern
The field profile of the optical wave traveling along the laser cavity manifests at the
laser facet as a 2D field distribution in the transverse vertical and lateral direction,
called the near-field pattern (NFP). The light emitted from the NFP spot propagates
BASIC DIODE LASER ENGINEERING PRINCIPLES
65
freely into space and the laser beam is strongly broadened in both directions by
diffraction. According to diffraction theory, the light spot some distance away from
the NFP is called the far-field pattern (FFP). The transition occurs at a distance
≈w2 /l 0 , where w is some characteristic full width of the NFP (Coldren and Corzine,
1995). The phase front of the mode is planar in the NF of index-guided waveguides
but approaches a spherical shape toward the FFP.
The FFP is characterized by the beam divergence angles at FWHM of the intensity
peak where θ ⊥ is the angle in the direction perpendicular to the active layer (so-called
fast axis) and θ is the angle parallel to the active layer (so-called slow axis). For
small angles the FFP is the Fourier transform of the NFP, or, in other words, the width
(angle) of a FFP is inversely proportional to that of a NFP in a good analogy to the
diffraction of light through a narrow slit.
Figure 1.28 illustrates these effects using two different NFPs of a simple ridge
laser. It shows also slow- and fast-axis FF intensity profiles of an InGaAs/AlGaAs
Figure 1.28 Schematic illustration of near-field (NFP) and far-field radiation patterns (FFP)
for a ridge laser with high aspect ratio (a) and low aspect ratio (b) between vertical and
horizontal beam divergence angle. (c) Radiation intensity distribution at different positions
along the optical cavity axis of a laser. (d) Transverse lateral and vertical far-field intensity
profiles of a single-mode InGaAs/AlGaAs laser measured at various optical output powers in the range of 100 to 300 mW. (e) Schematic diagrams for recording far-field intensity profiles with a rotating 1D small detector (left) and intensity maps with a 2D detector
array (right).
66
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
laser measured at different laser powers in the range of 100 to 300 mW and confirms
its fundamental transverse mode operation. Typical setups for measuring FFPs are
shown in Figure 1.28e. The NFP width w⊥ perpendicular to the junction plane depends
on the thickness and composition of various layers including the active, confinement,
and cladding layers. It can be approximated (Botez and Ettenberg, 1978; Agrawal
and Dutta, 1993) by
w⊥ ∼
= d(2 ln 2)1/2 0.321 + 2.1D −3/2 + 4D −6
(1.41)
where d is the active layer thickness and the normalized thickness D is given by
Equation (1.28). Equation (1.41) yields fairly accurate results for 1.8 < D < 6.
The NFP parallel to the active layer depends on the lateral guiding structure. For
an index-guided laser Equation (1.41) can be applied for w after replacing D by W,
where W is the normalized waveguide width given by (Agrawal and Dutta, 1993)
W = 2π
w 2
n
− n 2r,eff ,out
l r,eff ,in
1/2
.
(1.42)
Here nr,eff,in and nr,eff,out are the effective refractive indices within and outside of
the effective waveguide width w. The lateral NF for gain-guided lasers extends
considerably beyond the stripe width in contrast to index-guided lasers, where a
lateral index step as small as 0.005 is sufficient to confine the NF within the effective
active layer width.
The FFPs in the direction parallel and perpendicular to the active layer display the
spread of the laser mode and are important parameters in many applications requiring
well-defined divergence angles θ ⊥ and θ , for example, to couple laser light into
fibers. Also the FFP carries useful information because its shape and smoothness
depend sensitively on the type and strength of transverse vertical and lateral waveguiding, the type and number of excited spatial modes, and the quality of the waveguide material and interfaces regarding uniformity and structural irregularities. In
fundamental mode operation, the NFP and FFP display single-peak, smooth Gaussian
profiles, which become distorted when higher order spatial modes are present in the
laser operation.
The FF emission pattern for the fundamental mode of a symmetric vertical waveguide laser has a fast-axis beam divergence angle θ ⊥ , which is given to a good
approximation by the expression (Botez, 1982, 1981; Botez and Herskowitz, 1980)
2
1/2
0.65D n r,a
− n 2r,cl
θ⊥ =
1 + 0.15 1 + n r,a − n r,cl D 2
(1.43)
where nr,a and nr,cl are the refractive indices of the active and cladding layers,
respectively, and D is given by Equation (1.28). It is claimed that Equation (1.43)
supplies results accurate to within 3% for D ≤ 2, which corresponds to an active
layer thickness d ≤ 0.3 μm for an InGaAsP/InP DH laser emitting at 1.55 μm.
BASIC DIODE LASER ENGINEERING PRINCIPLES
67
An experimental value of 23◦ for a 1.3 μm InGaAsP/InP laser with d = 0.05 μm
compares well to the 20◦ calculated according to Equation (1.43) (Itaya et al., 1979).
Typical beam divergence angles of 980 nm, strained-layer InGaAs/AlGaAs
GRIN-SCH SQW ridge waveguide lasers are in the range of 20 to 35◦ for the
fast-axis and 5 to 10◦ for the slow-axis.
In Chapter 2, we will discuss the experimental and calculated dependencies of
the FF angles of a ridge InGaAs/AlGaAs laser on the composition and dimensions
of layers and structures including the AlAs mole fraction of the QW cladding, width
of the GRIN-SCH layer, width and depth of the ridge, and distance from the bottom
edge of the ridge to the active layer (called the residual waveguide thickness). The
insertion of so-called mode puller layers, such as inverse refractive index (IRIS) or
spread index (SPIN) structures, into the cladding layers to decrease the transverse
vertical FF angles, but to keep simultaneously the threshold current density low, will
also be discussed in Chapter 2.
We will also describe quantitatively the linking of FF angles to electrical and
optical laser parameters such as threshold current, efficiency, and maximum kinkfree optical power. All the above relations are crucial for optimizing this important
diode laser with respect to high-power and single-mode operation.
1.3.6
Fabry–Pérot longitudinal modes
To obtain the spectral separation between two adjacent longitudinal modes l m we
start from the phase condition ml 0 = 2Lnr,eff expressed in Equation (1.13), perform
the total differential, and then use the partial derivatives ∂nr,eff = (∂nr,eff /∂l 0 )∂l 0 ,
∂l 0 = l m , and ∂m = m = –1, which leads to a positive change l m of the
mode wavelength. After some simple algebraic manipulations we finally find for the
wavelength separation between two modes
lm =
2L n r,eff
l02
∂n r,eff
−
l0
∂l0
=
l02
2Ln r,gr,eff
(1.44)
where nr,gr,eff = nr,eff [1 − (l 0 /nr,eff )(∂nr,eff /∂l 0 )] is the effective index of the group
velocity vgr = c/nr,gr,eff of the longitudinal optical mode (c is the velocity of light in
vacuum). The group effective index in semiconductors is typically 20–30% larger
than the effective index, depending on the specific wavelength relative to the band
edge (Coldren and Corzine, 1995).
Figure 1.29 illustrates the formation of longitudinal modes along the cavity by
considering the Fabry–Pérot (FP) mode spectrum of the cavity and the gain versus
wavelength profile. Whenever the modal gain condition, Equation (1.32) or Equation
(1.36), is met at a certain FP wavelength l m , lasing starts at this wavelength and has
to comply with the phase condition, Equation (1.13). Only modes closest to the peak
gain are amplified, where the number of lasing modes depends on the width of the
gain maximum, and other modes are not excited because their losses are higher than
68
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.29 Schematic illustration of the formation of the laser longitudinal mode emission
spectrum and its dependence on gain spectrum and longitudinal Fabry–Pérot (FP) cavity modes.
the available modal gain. Mode spacings are, for example, <1 nm for InGaAsP/InP
lasers 300 μm long.
The wavelength of a lasing longitudinal mode shifts to shorter wavelengths by
a reduction of the refractive index induced by the injected carriers at a density N
(Casey and Panish, 1978; Sell et al., 1974). The size of the shift due to this so-called
plasma effect can be found by using the calculus of variation of Equation (1.13) which
results in
δlm (N ) =
l0 dn r
δN.
n r dN
(1.45)
Typical values for dnr /dN range from −1 × 10−21 cm3 to −6 × 10−21 cm3 for 0.85 μm
AlGaAs/GaAs and 1.55 μm InGaAsP/InP lasers, respectively (Casey and Panish,
1978; Nash, 1973).
On the other side, the lasing peak wavelength increases with increasing temperature caused by the Joule heating effects of the drive current, which include the
temperature dependence of the refractive index, bandgap energy, and cavity length.
Similar to Equation (1.45), we find for the mode wavelength shift caused by the
temperature dependence of the refractive index
l0 dn r
δT j .
δlm T j =
n r dT j
(1.46)
Here Tj is the junction temperature of the diode laser. Temperature coefficients of the
refractive index dnr /dTj are between 2 × 10−4 K−1 and 5 × 10−4 K−1 for common
IR diode lasers. Table 1.6 summarizes the mode wavelength shifts caused by the
temperature dependence of the refractive index and bandgap energy for some laser
material systems.
BASIC DIODE LASER ENGINEERING PRINCIPLES
69
Table 1.6 Lasing mode wavelength shifts caused by the temperature
dependence of the refractive index and bandgap energy (in brackets) for
some diode laser material systems in the infrared range.
δ λm/δTj
[nm/K]
Laser
material
Lasing wavelength
band [μm]
0.08 (0.25)
AlGaAs/GaAs
0.85
0.10 (0.40)
InGaAsP/InP
1.32
0.12 (0.60)
InGaAsP/InP
1.55
As can be seen from the table, the wavelength shift caused by the change of the
bandgap energy with temperature is about 3–5 times higher compared to that caused
by the refractive index change.
Finally, we want to mention the phenomenon of mode hopping. Steps can occur
in the emission wavelength versus injected current (temperature) plot, which can be
attributed to longitudinal mode hopping, at which the shift of peak gain causes the
dominant mode to change to an adjacent, higher wavelength longitudinal mode with
lower order number m, resulting in a wavelength shift of one FP mode spacing for
each mode hop. Mode hopping is suppressed until the gain at the adjacent mode
is higher than that at lasing. Mode hopping is manifested by small ripples or kinks
in the P/I characteristic, which can be very detrimental for certain applications of
single-mode diode lasers.
1.3.7
Operating characteristics
In this introductory section we give an overview of the electrical characteristics
based on optical output power P, voltage drop V across the laser, and drive current
I through the laser and comprising P/I and V/I curves, together with the derivative
characterizations, which include the characteristics dP/dI, d2 P/dI2 , dV/dI, and I dV/dI.
In the following four subsections, we then discuss laser efficiency, optical power, and
temperature characteristics along with the relevant expressions, and describe how
to measure internal parameters such as the intrinsic optical loss α i and quantum
efficiency ηi .
With increasing injection current, a diode laser is driven from a low bias state
with spontaneous emission to a state where stimulated emission is dominant enough
to generate sufficient gain to balance all losses for efficient light amplification. This
transition point occurs at laser threshold (Figure 1.30a). At threshold, the spontaneous emission clamps as the carrier density and thus the optical gain clamps
because most injected carriers are immediately converted to lasing light. This is due
to the stimulated emission process, which is much faster by a factor of 103 –104
than the processes of spontaneous and nonradiative recombination. In fact, the carrier density above threshold still increases with current with a slope τ stim /qd (see
Equation 1.34) determined by the stimulated emission lifetime and which is lower
70
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.30 Schematic representation of diode laser characteristics: (a) direct characteristics including power P versus current I and voltage V versus I; (b) injected carrier density
N versus input current I illustrating the clamping effect of the carrier density at threshold
causing the gain to clamp too; (c) derivative characteristics including four frequently used
derivative curves to investigate diode lasers; (d) simple setup for measuring diode laser optical
power/voltage/current characteristics.
by the above factor for the regime below threshold. Figure 1.30b illustrates the carrier clamping effect. Above threshold, the coherent emission power grows steadily
with current.
Below threshold, the V/I characteristic is similar to that of an ideal heterojunction
diode with a parasitic series resistance Rs comprising the contact resistance and
the resistance of the various layers. The voltage turns on when the applied voltage
exceeds the bandgap voltage of the active layer and rapidly increases, but above
threshold the voltage Vd across the diode laser saturates because the carrier density
saturates and the measured voltage drop V across the laser then becomes V = Vd + IRs
(Figure 1.30a).
The value of the measured threshold current depends on the applied evaluation
method. The methods are as follows: (i) linear fit: takes Ith at the point at which a
straight-line fit to the linear portion of the P/I curve above threshold intercepts the
current axis; (ii) two-segment fit: takes Ith at the point at which a straight-line fit to
the linear portion of the P/I curve above threshold intercepts the straight-line fit
to the linear portion of the P/I below threshold; (iii) first derivative: takes Ith at the
point at 50% of the maximum of the rising edge of the dP/dI curve; and (iv) second
derivative: takes Ith at the point at which d2 P/dI2 is a maximum (Hertsens, 2005).
BASIC DIODE LASER ENGINEERING PRINCIPLES
71
For commercial applications, it is important to note that the last three methods
are compatible with the standards Telcordia GR-468-CORE and GR-3010-CORE
(Telcordia Technologies, 2010).
There are four frequently used derivative curves calculated from the P/I and V/I
characteristics, which can be very useful in sorting out any nonlinearities showing up
in the P/I and V/I. Figure 1.30c shows a schematic representation of these derivative
characteristics, and Figure 1.30d shows a simple setup for measuring laser power,
voltage, and current.
In addition to the threshold current, the dP/dI versus drive current characteristic
also supplies the instantaneous slope efficiency above threshold and is sensitive to
nonlinearities and kinks in the P/I curve. A P/I kink is usually linked to a change in
the optical mode parallel to the active layer in the form of mode movement, mode
transition, or excitation of higher order modes. Also the turn-on of current leakage
paths at higher currents, which may lead to a rollover of the P/I can be identified with
the dP/dI.
The d2 P/dI2 curve is mainly used for determining the threshold current, but diode
laser manufacturers use it also to determine the exact location of the kink caused by
the activation of higher order transverse lateral modes in addition to the fundamental
mode. The location of the kink in the P/I gives the so-called kink-free optical power
up to that where the laser operates in the fundamental single mode and is a key
parameter for pumping fiber amplifiers with high single-mode power.
The dV/dI versus I plot supplies the dynamic resistance curve and is the effective
resistance to a change in current at a certain current. Typically, there is a downward
shift in this curve at lasing threshold separating the spontaneous emission operation
(light-emitting diode, LED) from the stimulated emission operation (diode laser).
The I dV/dI versus I plot is a powerful tool to measure series and parallel, linear
and nonlinear resistive circuit elements and to identify shunt current paths. As an
example, the information contained in the dV/dI drop at threshold can be quantified
by using the known V/I equation for an ideal diode with a series resistance Rs as
described above and given by I = Is exp{(q Vd )/(nk B T ) − 1}, and by taking the
derivative of the voltage across the laser V = Vd + IRs . Is is the saturation current and
n is the diode ideality factor. By neglecting the second term in the first expression
because the exponential term is usually much greater than one, we finally obtain
I dV/dI = nkB T/q + IRs for below threshold and I dV/dI = IRs above threshold (voltage
clamps because carrier density clamps). This means that the slope of I dV/dI versus
I curve is Rs above and below threshold, but there is a drop of nkB T/q at threshold.
In the presence of a shunt path across the diode laser, which can occur in strongly
index-guided lasers, investigations showed that a peak in the measured I dV/dI versus
I curve can be present before threshold is reached (Agrawal and Dutta, 1993; Wright
et al., 1982). From all these data, useful information about the junction characteristic
of the diode laser can be calculated, including ideality factor and contact resistance,
and laser manufacturers use these data for laser process control.
Finally, it should be mentioned that a kink in the P/I curve can generally also be
observed as a kink in the I dV/dI versus I characteristic. This can be understood from
the fact that a change in the optical mode changes also the average carrier density in
72
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
the active layer, which ultimately generates a change in voltage via the adjustment of
the quasi-Fermi levels.
1.3.7.1
Optical output power and efficiency
The power emitted by stimulated emission into the modal volume due to a current
density J > Jth can be written as
Pstim = A (J − Jth )
ηi hν
q
(1.47)
where A is the junction area and ηi is the internal differential quantum efficiency,
which represents the fraction of injected carriers that recombine radiatively and generate photons (cf. Equation 1.34 and accompanying text). Equation (1.47) expresses
the effective number of photons with energy hν generated in the modal volume per
second by the number of injected carriers per second. A fraction of this stimulated
power is dissipated inside the cavity via the distributed losses α i and the other fraction is coupled through the cavity end mirrors as useful laser output. These two
power fractions are proportional to the effective internal loss α i and mirror loss α m =
(1/2L)ln(1/R1 R2 ), and the output power (in units of W or mW) through both mirrors
can thus be written as a function of current above threshold
Pout
ηi hν
(I − Ith )
=
q
1
1
ln
2L R1 R2
[W or mW] .
1
1
ln
αi +
2L R1 R2
(1.48)
The ratio between the optical powers emitted at the two mirrors can be derived
as (Agrawal and Dutta, 1993)
(1 − R1 )
Pout,1
=
(1 − R2 )
Pout,2
R2
.
R1
(1.49)
For R1 = R2 we get Pout,1 = Pout,2 = 1 /2 Pout , and for all values of R1 and R2 the sum
of the two emitted powers is Pout , since a change in facet reflectivity does not affect
the total power, only its partition between the two facets. The power reflectivity of a
facet can be determined by using Equation (1.49).
The external differential quantum efficiency ηd is defined as the ratio of the photon
output rate to the photon generation rate that results from an increase in the carrier
injection rate
Pout
1
1
d
ln
αm
hν
2L R1 R2
= ηi
= ηi
.
ηd = 1
1
I − Ith
αi + αm
ln
α
+
d
i
2L R1 R2
q
(1.50)
BASIC DIODE LASER ENGINEERING PRINCIPLES
73
Inserting Equation (1.50) in Equation (1.48) we then get for the total output power
Pout =
hν
ηd (I − Ith ) [W or mW] .
q
(1.51)
While the external differential quantum efficiency is limited by energy conservation
to ηd < 1, the slope of the P/I characteristic, called slope efficiency ηsl , depends on
the lasing wavelength, and is given in units of W/A or mW/mA by
W
hν
1
dPout
mW
= ηd
= 1.24ηd
or
ηsl =
dI
q
l [μm] A
mA
(1.52)
where the wavelength l is measured in units of μm. Typical high slope efficiencies
at room temperature are in the range of 0.8 W/A for high-quality strained 980 nm
InGaAs/AlGaAs SQW lasers (Lichtenstein et al., 2004).
The overall net power conversion efficiency is an important parameter for determining the optical output power achievable from a given electrical input power.
The size of electrical power required to achieve a certain optical power is important,
because the dissipated power determines sensitively the strength of heating of the
laser during operation, which in turn impacts laser performance and reliability (see
Section 1.3.7.3 and Chapters 3–6). The electrical-to-optical conversion efficiency ηc ,
also called wall-plug efficiency, is simply the ratio between optical output power and
electrical input power, given as
hν
ηd (I − Ith )
αm
hν (I − Ith )
Pout
q
=
ηc =
= ηi
VI
I (Vd + Rs I )
q I (Vd + Rs I ) αi + αm
(1.53)
where we used for the terminal voltage across the laser V = Vd + Rs I with Vd being
the diode voltage and Rs a series resistance (see Section 1.3.7 above). According
to Equation (1.53), the series resistance is the main cause accounting for the small
discrepancy between the energy qV furnished to each injected carrier and the photon
energy hν. In practice, the applied voltage is slightly higher than the energy gap
voltage of the active layer Eg /q and can be well approximated by ≈1.4Eg /q. For
optimum coupling of light out of the cavity, α m can be made much larger than α i ,
and under these conditions ηc approaches ηi with the consequence that, if the internal
quantum efficiency is large, then the wall-plug efficiency can also be made large.
Conversion efficiencies for diode lasers have been increased above the 70% level in
recent years.
Government-funded programs such as the super high-efficiency diode sources
(SHEDS) program administered by the Defense Advanced Research Projects Agency
(DARPA, 2011) in the USA have set the goal to push the conversion efficiency to the
80% mark and beyond (Stickley et al., 2006).
In Section 2.4.5.3, we present a comprehensive discussion on diverse measures
to maximize optical output power and power conversion efficiency.
74
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.31 Experimental reciprocal differential quantum efficiencies versus cavity lengths
for compressively-strained In0.2 Ga0.8 As/Al0.3 Ga0.7 As GRIN-SCH SQW ridge lasers. The internal quantum efficiency ηi and internal optical loss α i were derived from the plot according
to Equation (1.54).
1.3.7.2
Internal efficiency and optical loss measurements
The external differential quantum efficiency ηd increases with decreasing cavity
length L and can be used to measure the internal quantum efficiency ηi and internal
optical loss α i . Using Equation (1.50) we obtain
1
1
=
ηd
ηi
1+
1
2αi
L =
ln 1/R1 R2
ηi
1+
αi
L
ln 1/Rm
(1.54)
where Rm = R1 = R2 is the mirror reflectivity assumed for simplicity to be equal
for both facets. Values for ηi and α i can be extracted from experimental data by
plotting measured values of 1/ηd versus L for lasers cleaved to different lengths,
where the reflectivities are known or calculated for uncoated mirrors according to
Equation (1.12). Values for ηd can be determined from Equation (1.52) by using
experimental values for the slope efficiency ηsl and lasing wavelength l. According
to Equation (1.54), the intercept of the plotted data with the 1/ηd axis gives 1/ηi and
the slope of the plotted data yields 2α i /ηi ln(1/R1 R2 ) or α i /ηi ln(1/Rm ), which can be
used with ηi to get α i .
Figure 1.31 plots a set of typical data taken from in-plane, 980 nm strained-layer
InGaAs/AlGaAs GRIN-SCH SQW ridge lasers, from which a distributed internal
optical loss coefficient α i ∼
= 2.2 cm−1 and internal quantum efficiency ηi ∼
= 92%
could be derived.
1.3.7.3
Temperature dependence of laser characteristics
Usually the threshold current increases and the slope efficiency decreases with increasing device temperature caused by laser self-heating at high drive currents or
ambient heating effects. Ideally, it is desirable to eliminate or at least minimize
BASIC DIODE LASER ENGINEERING PRINCIPLES
75
these detrimental temperature effects because they limit sensitively the application,
in particular, of high power lasers, and impact not only laser performance but also
laser reliability. The temperature dependence of the threshold current and the slope
efficiency can usually be described by the empirical expressions
Ith,2 = Ith,1 exp{(T2 − T1 )/(T0 )}
(1.55)
I2 = I1 exp{(T2 − T1 )/(Tη )},
(1.56)
and
respectively. Here T1 and T2 are two closely spaced temperatures with T2 > T1 , and
T0 and Tη are characteristic temperatures expressing the temperature sensitivity of the
threshold current and slope efficiency, respectively. The I terms in Equation (1.56)
denote the above-threshold-current increment required to obtain a desired output
power at both temperatures. Note that both characteristic temperatures are sensitively
related to laser materials, heterostructure design, and external parameters such as
laser length, width, facet reflectivities, and device heat sink efficiency. They usually
decrease as the laser junction temperature increases and smaller values indicate a
larger dependence of lasing characteristics on temperature.
In general, T0 values are higher in wider bandgap materials as opposed to lower
bandgap materials. Near room temperature, the experimental values are greater than
120 K for 850 nm GaAs/AlGaAs DH lasers compared to lower values in the range
≈50 to 70 K for InGaAsP/InP DH lasers emitting between 1.3 and 1.55 μm.
GaAs/AlGaAs QW lasers have higher values in the range ≈150 to 180 K and
strained InGaAs/AlGaAs QW devices furnished highest values of >200 K. Considering only the structure dependence of T0 , one can derive the general relationship
T0 (MQW) > T0 (GRIN-SCH) > T0 (SCH) (Weisbuch and Vinter, 1991). Experimental
values for Tη are typically higher by a factor of 2–3 than values for T0 : for example, T0 = 115 K and Tη = 285 K for 730 nm emitting InGaAsP/InGaAlP SCH
SQW lasers (Al-Muhanna et al., 1998). An example may illustrate the effect by
comparing the ratios of Ith at 20 ◦ C and 80 ◦ C for a GaAs/AlGaAs QW laser with
T0 = 160 K, and an InGaAsP/InP QW laser with T0 = 55 K. The threshold current
ratio amounts to Ith (80 ◦ C)/Ith (20 ◦ C) = 1.47 for the former and 2.78 for the latter. This indicates a greater variation in threshold current with temperature for the
InP laser.
The characteristic temperature is actually not a physical parameter but a fitting
parameter, which is linked to four main physical mechanisms, which can explain the
temperature characteristics, and which include an increase in the following parameters
with temperature:
r Gain width and hence a gain peak height decrease.
r Nonradiative recombination including Auger and processes via surface states
and deep levels.
76
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
r Optical losses including free-carrier and intravalence band absorption effects.
r Thermal escape of injected carriers over confining barriers into the confinement and cladding layers, and resistive leakage currents through blocking
layers.
Looking at Equation (1.35), we can identify three factors, namely, transparency
density Ntr , differential gain σ , and optical loss coefficient α a in the active layer,
which show a strong temperature dependence. Thermal broadening of carrier distributions due to the temperature dependence of the Fermi–Dirac function introduces
a temperature dependence in the parameters Ntr and σ , and can be written as Ntr ∝
T and σ ∝ 1/T, which means an increase of Ntr and decrease of σ , because electron
and hole energies are spread over a greater range at higher temperatures. Nonradiative recombination via temperature-activated defects and Auger processes will affect
the internal quantum efficiency ηi and cause a drop in ηi at higher temperatures.
Intervalence band and free-carrier absorption give rise to a temperature dependence
of both loss terms α a and α cl , which are proportional to temperature T to a good
approximation.
Thermal spillover of carriers over the heterobarriers, while not included explicitly
in Equation (1.35), has been found to be a substantial factor affecting the temperature
characteristics. Carrier leakage also reduces the internal quantum efficiency ηi and
its strength is very dependent on the materials and heterostructure used. It is smaller
in QW and strained QW than in bulk diode lasers due to the lower threshold current
density and higher confining barriers. With high threshold current devices the injected
carrier density pushes the quasi-Fermi level up, leading to a population of higher order
subbands in the well (band filling effect) with the consequence that the higher energy
carriers, especially electrons, easily escape from the active well into adjacent layers.
The occupancy of optical cavity states plays a decisive role in the difference between
MQW, GRIN-SCH, and SCH structures. The goal therefore includes reducing the
density of states at the energy levels most likely to be populated by hot carriers
escaping the active layer at elevated temperatures.
Even in optimized structures, the quasi-Fermi level is so high in the conduction
band that population of the cavity states occurs. It can be shown by calculation
that, at threshold, the number of carriers is about the same in the SCH optical
cavity and in the active layer, but only 20% of the carriers are in a GRIN-SCH
structure due to the reduced density of states in the triangular optical cavity (Weisbuch
and Vinter, 1991). It can also be shown that this detrimental population of optical
cavity states is lowest with MQW structures. In a MQW, the bulk density of states
(DOS) is the farthest away in energy and the high-energy tail of the Fermi–Dirac
distribution populates mainly the 2D-DOS of the well structure. In evaluating the
relative strength of carrier leakage, these DOS effects can be considered as the
primary causes for the relationship given above for T0 of MQW, GRIN-SCH, and
SCH lasers.
Auger recombination and intravalence band absorption are the major factors for
the reduced characteristic temperatures of low-bandgap InGaAsP/InP lasers. Carrier
leakage also plays a role due to Auger recombination, because hot electrons with
BASIC DIODE LASER ENGINEERING PRINCIPLES
77
energies higher than the band discontinuities are generated in the transition. Auger
recombination and intravalence band absorption can be mitigated by modifying the
valence band structure in strained QW structures (cf. Section 1.1.4.1). The Auger
recombination rate is also lower in a MQW than a SQW laser. This follows from
the fact that the Auger rate varies as N3 where the carrier density at threshold is
Nth ∼
=8 × 1017 cm−3 (Agrawal and Dutta, 1993)
= 2.5 × 1018 cm−3 for a SQW and ∼
for a MQW laser, leading to a lower Auger rate by a factor of 30 and a corresponding
improvement in T0 for a MQW laser. The internal optical loss can be reduced by using
QW structures due to the very low optical confinement and thus helps to improve the
temperature characteristics.
The key factors affecting the temperature characteristics of the slope efficiency
include free-carrier absorption and intravalence band absorption in the active layer and
confinement layers, with the effect of increasing the overall optical loss coefficient α i
and decreasing the internal quantum efficiency ηi with increasing temperature. Other
contributing factors such as Auger recombination and carrier overflow play a minor
role, because the rate of these processes is practically constant and independent of
temperature, since the carrier density is clamped at threshold and does not actually
change in the slope efficiency regime at current levels beyond threshold.
1.3.8
Mirror reflectivity modifications
Optimization of the diode laser performance requires modification of the intrinsic
power reflectivity of cleaved facets, which is about 0.32 for GaAs (cf. Equation 1.12),
by creating one end mirror with high reflectivity and the other facet with a low
reflectivity for coupling out the laser power. However, there are tradeoffs to be
considered, such as the threshold current decreases but the differential quantum
efficiency decreases too (cf. Equation 1.50) with increasing mean mirror reflectivity
(see Figure 1.32). To maintain a reasonable differential quantum efficiency one would
need to reduce the internal loss of the waveguide.
Figure 1.32 Plots of experimental threshold currents Ith (a) and front-facet differential quantum efficiencies ηd.ff (b) versus front-facet reflectivities Rff for ridge waveguide compressivelystrained InGaAs/AlGaAs GRIN-SCH SQW lasers 4 μm wide. Dashed lines are trendlines.
78
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
The reflectivity of cleaved facets can be modified by dielectric coatings. Coating the facets with appropriate thin dielectric layers has the additional advantage of
passivating and protecting the sensitive mirror facets from degradation effects and
thereby enhancing considerably the effective laser output and damage level. Chapters 3 and 4 will deal in detail with degradation modes and laser facet passivation
technologies. Figure 1.33a shows a typical coating of the low-reflectivity front mirror
and high-reflectivity back mirror for an edge-emitting, high-power FP diode laser.
It also illustrates the reflection and transmission of light at the interfaces of a single
dielectric film on a semiconductor. Stringent requirements are imposed on the optical
robustness of laser mirror coatings, which include:
r high transparency at the lasing wavelength;
r chemical, stoichiometric, and mechanical stability under high optical power
exposure and extreme environmental conditions;
r excellent adhesion to facet surface;
r ideally zero mechanical stress;
r prevention or suppression of gradual and sudden laser facet degradation mechanisms;
r high reliability and long lifetimes under application-specific conditions.
Figure 1.33 Schematic illustration of mirror coating approaches for high-power edgeemitting diode lasers. (a) Typical low-reflectivity front-facet single-layer coating and highreflectivity back-facet (BF) Bragg stack coating. (b) Reflection and transmission of light at
the surfaces of a semiconductor laser facet coated with a single dielectric film where rfa and
rsf denote the reflection coefficients at the surfaces of the film/air and semiconductor/film,
respectively. (c) Reflection and transmission at a Bragg mirror stack consisting of pairs (p =
number) of dielectric layers each a quarter-wavelength thick and each pair comprising a high
refractive index nr,f,h and low refractive index nr,f.l film.
BASIC DIODE LASER ENGINEERING PRINCIPLES
79
If there are no optical absorption and scattering losses in the dielectric, the power
reflectivity Rf of the single film with thickness df and refractive index n r, f can be
expressed by the equation for normal incidence
Rf =
rs2f + r 2f a + 2rs f r f a cos 2β
1 + rs2f r 2f a + 2rs f r f a cos 2β
(1.57)
where
rs f =
n r,s − n r, f
n r,s + n r, f
(1.58)
rfa =
n r, f − n r,a
n r, f + n r,a
(1.59)
2π
n r, f d f
l0
(1.60)
β=
and nr,s and nr,a are the refractive indices of the semiconductor and air, respectively,
and l 0 is the lasing wavelength in vacuum (Figure 1.33b). Equation (1.57) was derived
by Born and Wolf (1999 [originally 1959]) on the basis of the characteristic (transfer)
matrix for the film within the Fresnel reflectivity formalism for plane electromagnetic
waves. Changes for the modal reflectivity of a diode injection laser are expected to
be no greater than 15% (Ikegami, 1972). The reflectivity in Equation (1.57) changes
periodically with β, that is, with a periodicity in thickness of l 0 /(2n r, f ) of the
dielectric film. The maximum value of Rf can be found when cos 2β = 1, that is, for
thicknesses df = ml 0 /2n r, f (for m = 1, 2, 3, . . .) and becomes for normal incidence
R f max =
n r,s − n r,a
n r,s + n r,a
2
(1.61)
which is independent of n r, f . Rfmax is the natural reflectivity for an uncoated mirror.
The minimum value of Equation (1.57) is achieved at cos 2β = −1, that is, for
thicknesses df = ml 0 /4n r, f (for m = 1, 3, 5, . . . ) and becomes for normal incidence
R f min =
n r,s n r,a − n r,2 f
n r,s n r,a + n r,2 f
2
.
(1.62)
This equation gives the condition for an anti-reflective coating, which would be
strictly achieved at normal incidence for
n r, f =
√
n r,s n r,a .
(1.63)
An effective anti-reflective (AR) coating on a 980 nm InGaAs/AlGaAs laser
facet can be achieved by depositing a thin Al2 O3 film of thickness df = ml 0 /4n r, f
80
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.34 (a) Plot of the reflectivity Rf versus Al2 O3 film thickness df calculated according
to Equation (1.57) for the low-reflectivity front facet of a 980 nm InGaAs/AlGaAs laser. A 10%
front-mirror reflectivity can be achieved at a thickness of 190 nm. (b) Calculated reflectivity
Rf versus wavelength l for 140 nm Al2 O3 film thickness as found at the first minimum in the
Rf versus df dependence in (a). The minimum in (b) is close to 980 nm as expected.
(for m = 1, 3, 5, . . .), because Al2 O3 with an index n r, f ∼
= 1.76 at a wavelength
of 980 nm meets the condition in Equation (1.63) well by using nr,s ∼
= 3.28 for
Al0.3 Ga0.7 As. Al2 O3 has all the properties expected from an effective, efficient, and
reliable mirror coating material (see above).
Figure 1.34a plots the reflectivity versus Al2 O3 film thickness calculated according to Equation (1.57) for the low-reflectivity front facet of a 980 nm InGaAs/AlGaAs
laser. As expected, the periodic dependence has a periodicity in thickness of l 0 /(2n r, f )
and the maxima and minima points are close to 29% and 0.1%, respectively. A 10%
front-mirror reflectivity can be achieved at a thickness of 190 nm. The reflectivity
versus wavelength dependence calculated for 140 nm Al2 O3 thickness, as found at
the first minimum in the Rf versus df dependence, is plotted in Figure 1.34b. The
minimum in the figure is close to 980 nm as expected.
Periodically stratified films are highly reflective coatings. They are formed by
so-called Bragg stacks, which are pairs of films with high n r, f,h and low refractive
index n r, f,l and a thickness of each film set at a quarter-wavelength of l 0 /4n r, f (see
Figure 1.33c). The constructive interference in the multilayer stack results in dramatically high reflectivity values, which can be increased close to unity by increasing the
number p of periods of double films and the index ratio nr,f,h /nr,f,l between the high
and low refractive index films. For normal incidence the reflectivity of such a Bragg
reflector has been derived by using the transfer matrix method (Born and Wolf, 1999)
and is given by
⎛
Rstack
n r, f,h
n r,s
n r, f,h
n r,a
n r, f,h
n r, f,l
2 p ⎞2
⎜1 −
⎟
⎜
⎟
=⎜
2 p ⎟ .
⎝
⎠
n r, f,h
n r, f,h
n r, f,h
1+
n r,s
n r,a
n r, f,l
(1.64)
BASIC DIODE LASER ENGINEERING PRINCIPLES
81
Figure 1.35 Spectral reflectivity of a periodic multilayer Bragg reflector calculated for the
high-reflectivity back mirror of a 980 nm InGaAs/AlGaAs laser. Two pairs (p = 2) of quarterwavelength-thick Al2 O3 and a-Si layers provide a high reflectivity of >90% in a broad wavelength range ∼850 to 1200 nm with a maximum of 94% at 980 nm.
The spectral reflectivity has been calculated with Equation (1.64) for the highreflectivity (HR) back mirror of a 980 nm InGaAs/AlGaAs laser by using the standard
coating materials of Al2 O3 with nr,f,l = 1.76 and a-Si (amorphous-Si) with nr,f,h =
3.69 (Ioffe Physico-Technical Institute, 2006). Figure 1.35 shows a reflectivity of
0.76 for p = 1 and 0.94 for p = 2 at l = 980 nm. A reflectivity of ≥0.9 is achieved
in a rather broad wavelength range ∼850 to 1200 nm. Alternative coating material
combinations of TiO2 (nr,f,h = 2.78) with SiO2 (nr,f,l = 1.45) offer the advantage
of developing reduced facet heating by laser light absorption due to the negligible
absorption of TiO2 at wavelengths 450 nm. However, due to the lower index of
TiO2 , three periods, p = 3, would be required to obtain a reflectivity > 90%.
1.4
Laser fabrication technology
The purpose of this section is to give a brief overview of key steps for fabricating edgeemitting laser devices including laser wafer growth, processing, and packaging. While
a variety of epitaxial growth techniques have been used to grow diode lasers, the two
most important techniques for the growth of high-power diode lasers for both research
and commercial applications are molecular beam epitaxy (MBE) and organometallic vapor-phase epitaxy (OMVPE), also referred to as metal–organic chemical vapor
deposition (MOCVD). MOCVD, which comes in low-pressure (∼0.1 atm) and atmospheric pressure systems, uses metal–organic precursors such as group-III alkyls and
group-V hydrides as gas sources to react on a heated substrate to form the epitaxial
film. In contrast, MBE is carried out under ultrahigh vacuum (UHV; <10−10 Torr)
with thermal beams of atoms evaporated from heated effusion cells and directed to the
atomically flat and contaminant-free surface of a substrate held at high temperature
to form the layer.
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SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
In the following, we focus on the MBE technique and describe some of the major
issues, which have to be considered in the growth of a standard InGaAs/AlGaAs
GRIN-SCH SQW laser structure on n-GaAs substrates. We also discuss the key steps
to be taken in processing the laser wafer to fabricate a finished ridge waveguide diode
laser chip (cf. Section 1.3.5.2 and Figure 1.26; see also Sections 2.1.3 to 2.1.6). Finally,
we discuss diode laser packaging issues with an emphasis on single-mode, in-plane
diode lasers along with associated materials, processes, and components, common
package designs including optical alignment and coupling, thermal management, and
atmosphere control requirements inside the package.
1.4.1
Laser wafer growth
UHV analysis techniques that can be applied include reflection high-energy electron
diffraction (RHEED), Auger analysis, and mass spectrometry for monitoring the
growth rate and studying the layer characteristics; the latter can also be achieved by
optical techniques such as reflectometry. Usually the growth temperature is monitored
by a single-wavelength optical pyrometer in conjunction with a thermocouple to
provide a complementary temperature reading. The UHV conditions are maintained
by ion pumps, cryopumps, and titanium sublimation pumps, and, in addition, liquidnitrogen-filled cryoshrouds surround the effusion cells and the substrate to protect
the substrate from any contamination by impurities.
1.4.1.1
Substrate specifications and preparation
Usually n-type GaAs substrates ≥2 inches with a (100) orientation are used. However,
misorientations such as 2◦ toward the 110 direction reduce the formation of loop
dislocations at the substrate/epitaxial layer interface, or 3–4◦ toward 111A yield a
reduced incorporation of impurities like oxygen in AlGaAs, and smoother and sharper
heterointerfaces (Chand et al., 1994). The substrates are silicon doped, typically
1.5 × 1018 cm−3 , and have a low dislocation density measured by the density of etch
pits of <2 × 103 cm−2 . Slight substrate misorientations and lower defect densities
result in improved laser performance and lifetimes.
The substrates are cleaned to remove any contamination layer on their surfaces.
The process is performed in a class 100 clean-room environment and includes the
following steps: cleaning in sulfuric acid, rinsing in flowing deionized water, etching
in a solution of deionized water with ammonia and hydrogen peroxide, and final
rinsing in deionized water. Each of these steps lasts between 1 and 2 min. The
substrate is dried either by blowing dry with a nitrogen gas gun or by spinning in
a spin processor, and then returned into the original container or loaded into the
MBE system.
1.4.1.2
Substrate loading
Loading and unloading the growth chamber is achieved via a UHV buffer and load–
lock chamber to minimize the introduction of detrimental impurities such as oxygen
BASIC DIODE LASER ENGINEERING PRINCIPLES
83
and water into the actual growth chamber. The load–lock is pumped to UHV conditions. A stress-free mounting of the substrate in the holder and a smooth transfer
inside the system are required to ensure defect-free growth.
1.4.1.3
Growth
In a solid-source MBE, group-V elements are much more volatile than group-III
elements. This effect is used for stoichiometry control where usually the substrate
temperature is kept sufficiently low to increase the group-III element sticking coefficient (fraction of atoms in the beam sticking to the substrate) close to unity. The
growth rate is then determined by the group-III element flux and the group-V element
flux is adjusted to multiple times of that flux. A typical V/III (e.g., As4 /Ga) beam
equivalent pressure ratio p As4 / pGa is 25. The sticking coefficients for all the components have to be determined empirically as a function of substrate temperature and
beam flux. Substrate temperatures Tsub for AlGaAs growth have to be high, in the
range ∼
=700 to 720 ◦ C, to avoid the formation of deep-level defects and nonradiative
recombination centers (As et al., 1988). In contrast, the growth temperature for the
InGaAs QW is ∼
=510 ◦ C, which requires a growth interruption just prior to the QW
growth to allow the temperature to decrease from the higher temperature at AlGaAs
growth to the lower value required for the QW growth. It is known that there is a
tradeoff between the optimum V/III ratio for AlGaAs and InGaAs growth: InGaAs
prefers a lower ratio (lower As4 flux) whereas AlGaAs growth quality degrades if the
flux is too low. Useful As4 beam equivalent pressure values are ∼0.8 × 10−5 Torr and
∼1.2 × 10−5 Torr for optimum growth of InGaAs and AlGaAs, respectively, which
can be achieved, for example, by rapid switching between two separate As effusion
cell sources for depositing the two materials at different As fluxes.
To establish a safe operating regime with optimum and stable laser parameters it
is essential to know the sensitivity of key growth parameters such as temperature and
As4 pressure on laser performance parameters like threshold current density Jth and
internal quantum efficiency ηi . Experiments yielded the following results (Epperlein,
1999): roughly linear dependencies of
r Jth on Tsub with a slope of −40 A/cm2 per 10 ◦ C and ηi on Tsub with a slope
+ 0.03 per 10 ◦ C for ± 10 ◦ C range of change in standard growth temperature;
and
r Jth on p As with a slope of + 45 A/cm2 per 1 × 10−5 Torr and ηi on p As with
4
4
a slope of −0.04 per 1 × 10−5 Torr for a range of change of twice the standard
As4 beam equivalent pressure.
By considering the above relationships and many other necessary dependencies
and procedures such as the generation of growth parameter calibrations, effusion
cell outgassing protocols, and initial growth conditions (details are beyond the scope
of this book), the laser growth program has to be established and finally run and
controlled by computer. The program details the exact growth conditions, including
growth times, temperature ramp functions, effusion cell temperatures, and shutter
84
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
modulations used during the growth for each building block in the vertical structure to enable precisely controlled and reproducible layer thicknesses, compositions,
and doping profiles. The layer sequence includes a thin GaAs buffer layer on top
of the substrate surface, first cladding grading, n-AlGaAs cladding layer, AlGaAs
GRIN-SCH layer with embedded InGaAs QW, p-AlGaAs cladding layer, second
cladding grading, and p + -contact layer. Several different short AlGaAs/GaAs superlattices are positioned at specific locations in the structure, each with its own
purpose, such as to getter segregating surface impurities, to trap diffusing ions at
heterojunction interfaces, to block threading dislocations, or just to serve as a useful
marker in scanning electron microscopy (SEM) investigations to determine layer
thicknesses.
1.4.2
Laser wafer processing
1.4.2.1
Ridge waveguide etching and embedding
One of the most critical processing steps is the formation of the ridge waveguide
structure because it determines the final optical laser parameters such as FF angles
or the maximum kink-free optical output power and electrical parameters like the
threshold current. The lateral waveguide pattern is defined by a standard lithographic
process and then transferred to the (Al)GaAs layers by wet chemical etching. The
requirements for control over etch depth and ridge profile are extremely stringent
and include control of the former to within a few tens of nanometers (see Chapter 2).
This can be achieved by suitable, epitaxially grown etch-stop layers or by precise
adjustment of the etch solution and etching in several steps with intermediate depth
control measurements. The etched ridge is embedded with a dielectric insulator such
as Si3 N4 deposited by a low-temperature plasma-enhanced chemical vapor deposition
(PECVD) technique, but leaving uncovered the highly doped p + -GaAs layer on top
of the ridge used for the formation of the Ohmic contact. The dielectric layer is
structured by a lift-off process. Ideally, waveguide etching and dielectric embedding
are fully self-aligned processes. In Chapter 2, we will discuss within the single
spatial mode issue other lateral waveguide formation technologies including QW
intermixing, epitaxial regrowth, or the use of photonic crystals.
1.4.2.2
The p-type electrode
The structure of the p-electrode is formed by using another lithographic process,
evaporative metallization and resist lift-off. A Ti/Pt/Au contact is evaporated at an
angle to ensure good metal step coverage over the ridge and to minimize the stress
level in the Pt film. It is nonalloyed to avoid interdiffusion of the metallic species. A
thin Ti layer acts as an adhesion promoter, Pt is used as a diffusion barrier for Au, and
Au is used for the top contact layer. The barrier effectiveness depends strongly on the
crystalline fine structure and stress in the Pt film, which are strongly determined by the
deposition method and process parameters of the contact. The p + -GaAs contact layer,
highly doped to ≥2 × 1019 cm−3 , has to be kept free of damage and contamination
BASIC DIODE LASER ENGINEERING PRINCIPLES
85
Figure 1.36 Schematic cross-section of a ridge waveguide structure illustrating the ridge
protecting function of a thick patterned gold layer electroplated on the p-electrode of the
wafer. Layer thicknesses and lateral dimensions not to scale.
before depositing the metal layers to ensure low specific contact resistivity in the
regime 1 × 10−6 cm2 . For further details, see Section 3.1.1.4 and Figure 3.2.
1.4.2.3
Ridge waveguide protection
It is advisable to deposit a thick ridge protective layer on the p-side of the wafer,
which can be accomplished by electroplating Au using a patterned photoresist as
a cast. Positive features of the some micrometer thick Au layers include protecting
the ridge from mechanical damage during processing and handling, and providing
more effective spreading of heat generated during laser operation. The waveguide
protection layer also eases mounting of the laser chip p-side down onto a heat sink
carrier. However, there are also negative effects, such as the generation of stress in
the laser chip reaching typical levels of 2 × 108 dyn/cm2 for as-plated Au due to the
large thickness of the layer. Figure 1.36 shows schematically a cross-section of the
ridge waveguide including the dielectric ridge embedding layer, n- and p-electrode
layer, and thick Au ridge protective structure.
1.4.2.4
Wafer thinning and the n-type electrode
The back-side processing of the wafer comprises thinning of the wafer and deposition
of the n-side electrode material. Thinning down to a thickness of about 100 μm is
carried out by a lapping process in an Al2 O3 slurry. The wafer is mounted with the
protected p-side onto a glass lapping carrier by using a special wax. Protection of the
p-side with the sensitive ridge structure is achieved by depositing before lapping a thin
layer of polyimide, which is known for its excellent planarizing properties. Thinning is
required mainly for two reasons, to facilitate a proper, defect-free cleaving of the laser
facets and to reduce the thermal resistance of p-side-up mounted laser chips. After
lapping, the n-side of the wafer is chemically etched to remove any lapping damage,
yet not smooth enough to adversely affect adhesion of the n-metallization. The
n-electrode consists of a standard AuGe/Ni/Au metal layer scheme and is evaporated
onto the large substrate back-side area with subsequent alloying at high temperature
below the Au/Ge eutectic point. This is to alloy the metal contact with the highly
doped substrate material to deliver low-resistance metal contacts and to mitigate
86
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
stress levels. According to standard practices, the n-contact is then strengthened by
evaporating a second layer of metal to allow for good solderability of the laser die to
a package submount.
1.4.2.5
Wafer cleaving; facet passivation and coating; laser optical
inspection; and electrical testing
The final back-end-of-line (BEOL) processing steps are as follows:
r Cleaving the wafer along crystallographic planes into bars with typical lengths
of 10 mm comprising 40–80 laser chips with widths ∼
= 100–250 μm and lengths
∼
= 500–3000 μm (equal to bar width) depending on laser type and application.
r Passivating the cleaved facet surfaces immediately after cleaving to minimize
detrimental corrosion effects. For details see Section 4.2.
r Coating the passivated facets to modify their reflectivity and to make them
robust against any degradation mechanisms. The coating process is usually
carried out in a PECVD or ion beam (IB) sputter deposition system depending
on the actual coating material and passivation technique used. Selection of the
material and thickness of the passivation layer is also determined by the fact
that the PECVD process involves ions with much lower energies than the IB
process. High-energy ions can damage irreversibly on impact a thin passivation
layer a few nanometers thick. For details see Sections 1.3.8 and 4.2.3.
In Section 1.3.8, we discussed in detail reflectivity modification schemes including (i) the impact of reflectivity changes on major laser parameters, (ii) the requirements on the coating material, and (iii) quantitative expressions for calculating the
required reflectivity values.
Chapters 3 and 4 will deal extensively with the physical effects linked to facet
passivation and with potential passivation techniques including nonabsorbing mirror
schemes. The finished devices are examined under an optical microscope for appropriate mechanical integrity and then electro-optically tested, usually on the bar level.
Depending on the application, single laser chips cleaved from the bars or complete
laser bars are mounted in appropriate packages fit for use for electrical input/output
and optical output via electrical terminals and the optical port.
1.4.3
Laser packaging
This is a comparatively brief section to conclude the chapter. In this section, we
will look at some basic material, thermal, electro-optical, chemical, and geometrical
requirements for packaging high-power diode lasers with a focus on single-emitter,
single-mode, in-plane devices, and will refer to some current generic and new package
designs for illustration, and address in particular soldering, optical alignment, coupling efficiency, and temperature control issues. Packaging greatly influences laser
device performance and reliability.
BASIC DIODE LASER ENGINEERING PRINCIPLES
87
Figure 1.37 Schematic cross-sectional view of two typical, hermetically sealable diode laser
package formats for low to high output power applications. (a) Basic coaxial type TO can for
devices up to 5 W with the option to attach and align a fiber to the can and include a lens, TEC,
photodiode, and thermistor (not shown) in multi-pin formats. (b) Typical rectangular butterfly
package, which is an industry standard 14-pin DIL fibered package for applications up to about
5 W laser power by using a high-performance internal TEC.
1.4.3.1
Package formats
Commercially available diode lasers come in a wide variety of package formats.
The vast majority of lower performance and cost-sensitive devices come in lower
cost package formats, such as transistor outline (TO) can header packages. Highperformance laser products including high-power pump lasers and most dense wavelength division multiplexing (DWDM) optical communications signal lasers are
assembled and fiber pigtailed in hermetically sealed 14-pin butterfly packages or
mini-dual in-line (mini-DIL) packages, just to mention the most common ones. An
interesting new development is a low-profile, uncooled, hermetically sealed, and low
thermal resistance optical flat package (OFP) for low-cost and high-reliability applications, which has a much smaller footprint and lower cost bill of materials (BOM)
than the 14-pin butterfly and can handle up to 6 W of optical output from the fiber
(Singh et al., 2004). For illustration, cross-sectional schematic views of two typical
packages are displayed in Figure 1.37. The following subsections describe the basic
components and technologies related to diode laser packaging.
1.4.3.2
Device bonding
Device chip bonding, which means soldering the laser die on a monolithic planar heat
sink substrate, is the first step in assembly of the package. Usually single-mode laser
chips are soldered p-side up directly to the metallized heat sink material, whereas
88
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Table 1.7 Room temperature thermal conductivities and expansion
coefficients of typical heat sink materials used for mounting optoelectronic
devices. Data for the listed semiconductors are for comparison.
Material
Thermal conductivity
at 300 K [W/(m K)]
Diamond
AlN
SiC
Al2O3
BN
GaAs
InP
Si
Ag
Cu
Al
W90Cu
W75Cu
Mo70Cu
Mo50Cu
2000
26
70
17
600
54
70
150
422
402
226
185
230
195
235
C nanotubes
Thermal expansion
coefficient [ppm/K]
2.3
4.2
3.7
6.5
3.7
6.6
4.5
2.6
19.2
17.6
23.4
5.9
9.8
8.1
10.4
~3000
high-power multimode lasers and laser bars are soldered p-side down onto the heat
spreader. The heat sink material should have a thermal expansion coefficient close
to that of the laser die and a high thermal conductivity; in addition, high electrical
resistivity is required for high-frequency applications. Table 1.7 lists some common
heat sink materials where AlN and CuW are the most popular ones for packaging
diode lasers. Some data are from Fukuda (1999). As most heat sink materials are
electrical insulators, they have to be metallized by depositing metals such as Ti/Pt/Au
or Cr/Au to enable an effective and reproducible solder joint process.
The bonding configuration strongly influences the temperature characteristics of
the laser where a crucial factor is the wetting capability of the solder, which means the
adhesion between the base metal and liquid solder. Normally, soldering is required to
be flux free to prevent contamination and degradation of the facets and to assure longterm reliability. In addition, in order to prevent hot spots under high-power operation,
because of the poor lateral heat conduction within the laser die, the soldering process
has to be void free.
Two groups of solder metals are used: soft solders, which have low melting points
(MPs), and hard solders with high melting points. Typical representatives for the first
group are In–52 wt% Sn (MP = 117 ◦ C), Sn–60 wt% Pb (MP = 183 ◦ C), and for the
second group Sn–20 wt% Au (MP = 280 ◦ C) and Au–88 wt% Ge (356 ◦ C) (Fukuda,
1999). Hard solders generally cause a larger mechanical stress at the bonded part due
to their higher bonding temperature, whereas soft solders absorb the mechanical stress
built up at the interface between the laser die and heat sink during soldering, because
BASIC DIODE LASER ENGINEERING PRINCIPLES
89
they deform plastically under stress. However, soft solders become unstable during
long-term laser operation, because of thermal fatigue and creep which increases in
strength with decreasing melting point and when the mechanical stress is stronger
than the solder’s elasticity limit. This degradation and creep of the solder sensitively
impacts the coupling efficiency of the laser light into a fiber. On the other hand,
hard solders such as Au-rich AuSn enable long-term and reliable stability of the
bonded laser die. However, AuSn shows very little creep, which may be a concern,
because thermal expansion mismatches, for example, between the laser submount and
the structure underneath, almost invariably lead to some degree of warpage, which
cannot be allowed to vary with time in service. The mechanical stress per unit length,
Sbond , can be approximated by (Fukuda, 1999)
Sbond = |αHS − αdie | (Tbond − Tamb ) E Ym
(1.65)
where α HS and α die are the thermal expansion coefficients of the heat sink and laser
die, respectively, Tbond is the bonding temperature, which is close to the melting point
of the solder, Tamb is the ambient temperature, and EYm is Young’s modulus of the
laser die.
An example should demonstrate the effect: bonding a GaAs laser die to an AlN
material generates a compressive stress in the die at 25 ◦ C of ∼
= 6 × 108 dyn/cm2
◦
when a hard solder such as Au-rich AuSn (Tbond ∼
= 2 × 108
= 280 C) is used and ∼
2
◦
dyn/cm when the soft solder InSn (Tbond ∼
= 120 C) is used. Here we also used
6.6 × 10−6 ◦ C−1 and 4 × 10−6 ◦ C−1 for the thermal expansion coefficient of GaAs and
AlN, respectively, and 8.6 × 1011 dyn/cm2 for Young’s modulus of GaAs. The stress
generated in the die with soft solders can easily be released via plastic deformation
into the solder layer, whereas high mechanical stress levels in excess of 109 dyn/cm2
caused by hard solders cannot be released into the hard solder, but will trigger the
growth of slip dislocations in the laser chip, which will impact its performance and
reliability.
1.4.3.3
Optical power coupling
Many diode laser applications require, but also prefer, fiber delivery systems, where
the laser beam is coupled into an optical fiber to transport the light to the application.
The incident (acceptance) angle of light into a step index fiber with a core
refractive index nr,co larger than the index nr,cl of the cladding has to be such that the
beam reaches the core–cladding interface at an angle ≥ θ cr , the critical angle for total
reflection, in order to be captured and propagated as a bound mode. The geometry of
light coupling into an optical fiber is illustrated in Figure 1.38.
The light-capturing capability of the fiber can be expressed by the fiber numerical
aperture (NA), which is the sine of the largest angle θ a contained within the cone of
acceptance and is given as
NA = sinθa
(1.66a)
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SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
cladding
θa
core
θcr
θc
cladding
nr,cl
nr,co > nr,cl
nr,cl
Figure 1.38 Schematics for calculating the numerical aperture of a step-index optical fiber.
Correlation between acceptance angle θ a cone and critical angle θ cr for total reflection at the
fiber core/cladding interface.
and using Snell’s law we obtain after some manipulation
NA =
n 2r,co − n 2r,cl
NA = n r,co sinθc
(1.66b)
(1.66c)
where θ c = 90◦ − θ cr is the supplementary angle for total reflection. Equation
(1.66c) is a useful expression for the NA and relates it to the index of the core and
the maximum angle at which a bound ray may propagate. The acceptance angle θ a
is then given by
θa = arcsin (NA) = arcsin
n 2r,co − n 2r,cl .
(1.67)
Typical NA values for single-mode (SM) and multi-mode (MM) fibers are 0.1
and 0.2–0.3, respectively. The higher the NA, the more modes in the fiber, which
means the larger the dispersion of this (MM) fiber. The higher the NA of an SM fiber,
the higher its attenuation, because a significant proportion of optical power travels in
the cladding, which is highly doped to achieve a high index contrast for SM.
In the following, we discuss the optical requirements to achieve the highest
possible coupling of optical power from an SM diode laser into an SM optical
fiber. This can be achieved by matching both the amplitude and phase of the laser
mode to the amplitude and phase of the fiber mode. Technical realizations including
quantitative coupling efficiencies, dependencies, and alignment tolerances will also
be discussed.
In Section 1.3.5.3, we discussed how light emitted from the usually elliptical NF
spot propagates freely into space and broadens strongly in both directions by diffraction – stronger in the transverse vertical than transverse lateral direction. Important
information about setting up quantitative conditions for mode matching can be obtained by determining the laser mode field radii (1/e2 intensity points) and wavefront
BASIC DIODE LASER ENGINEERING PRINCIPLES
91
Figure 1.39 (a) Mode field radii of an InGaAs/AlGaAs ridge laser calculated as a function
of the axial distance from the facet for the transverse vertical (solid line) and transverse lateral
(dashed line) direction. (b) Laser wavefront curvature radii calculated as a function of the axial
distance from the facet for the transverse vertical (solid line) and transverse lateral (dashed
line) direction.
radii of curvature (measure for phase) as a function of the axial distance from the
laser facet for transverse vertical and transverse lateral directions.
Figure 1.39a shows the mode field radii versus axial distance calculated for
a narrow-stripe laser (Epperlein et al., 2000). As expected, the mode field radii
increase with increasing axial distance, faster in the transverse vertical direction with
a linear increase for 5 μm in this example. The FF angles can be taken from the
asymptotic angles in the transverse vertical and lateral directions and are ∼
=22◦ and
◦
∼
=6 μm where the transverse
=9 , respectively, in this case. Both curves intersect at ∼
vertical and lateral mode field radii are the same and hence the amplitude distribution
is circular (see Figure 1.28c).
The shapes of the phase fronts also change in the axial direction with the phase
constant at the facet, which is expressed by the large radii of the wavefront curvature
in both directions (Figure 1.39b). At large distances the radii of curvature become
equal to the axial distance, which means that the phase fronts are spheres centered at
the facet. For both directions, the radii have minima at different locations in the case
of an elliptical NF spot, whereas for circular intensity distributions the locations of
the minima are the same. The distance from the facet to the minimum is called the
Rayleigh range and marks the division between the NF and FF.
From Figure 1.39 we can see that there are two locations where matching the
phases and amplitudes of the laser mode and fiber mode (expressed by the mode
field radius, which is half the distance between the points in the fiber where the
electric field amplitude decays to 1/e of its peak value) can be done best. At the facet,
the phase of the laser mode is planar and therefore only the amplitude needs to be
matched to the fiber, which can be accomplished by using an elliptical core fiber in
case the NFP is elliptical. The laser phase is only planar very close to the facet, which
requires the fiber to be located very close to the facet to achieve high coupling. The
other place is at the crossover point (Figure 1.39a) where the amplitude distribution
is circular.
92
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Mode amplitude matching can be achieved by selecting a fiber with a mode field
radius, which equals that of the laser (∼
= 2 μm in the example). Figure 1.39b shows
that mode matching is not that straightforward at the mode field radii crossover
point, because the radii of curvature in both directions are very different at this point
(∼
= 6 μm in the transverse vertical and >40 μm in the transverse lateral direction in
the example). However, over the core of the fiber (∼
= 2 × 2 μm = 4 μm) the phase
fronts are to a good approximation cylindrical and to match them a cylindrical lens
is required, which is best realized by a fiber tipped with a wedge lens.
In summary, by placing a wedge-lensed fiber, which has a mode field diameter
equal to the diameter of the laser intensity distribution at the position where the
intensity distribution is circular, both the phase and amplitude of the modes can be
matched. The best form for the wedge is a hyperbola; however, a simple wedge
or double wedge is easier to fabricate and can match the phase sufficiently well to
realize high (>80%) coupling efficiencies, in case the mode amplitude is also well
matched. If the laser mode is circular, the best form for the phase matching lens is
a hyperboloid, which can be well approximated by a cone, equivalent to the simple
wedge lens in the case of an elliptically shaped NF (laser mode). It should be pointed
out that the lens only serves to match the phase.
Bulk optical systems can be used when the beam is allowed to expand to a size
that is considerably larger than the fiber mode field diameter and is then focused
with a discrete lens. The best lenses are aspheric lenses that can be designed to have
no spherical aberration and hence phase matching should be good; however, they
cannot match the elliptical spot of the laser to the standard circular core of the fiber,
because they magnify equally in vertical and lateral planes and therefore a cylindrical
or acylindrical lens would have to be added to correct this. There is, nevertheless,
a very smart commercially available solution (Blue Sky Research, Inc., 2010). A
diffraction-limited acylindrical μLensTM placed directly in front of the laser captures
nearly 100% of the emitted power and converts the divergent elliptical output beam
into a beam with a spherical wavefront and nearly circular profile. The beam behaves
as if it was emitted from an ideal point source with a certain low divergence angle,
and, if required, can then be precisely focused to a round spot using bulk optics.
To optimize coupling efficiencies, the optical coupling system comprising active
and passive elements has to be aligned either passively or actively. In active alignment,
the alignment between the components is performed under operation of the laser,
whereas in passive alignment, the laser is not operated and the components are
mounted on bonding pads patterned on the submount or heat sink.
Single-mode diode laser packaging invariably involves active alignment along a
total of six axes, mainly due to manufacturing variances in the laser, laser assembly,
and optical fiber core center. The various elements are aligned and fixed one by one
and the monitored optical power is maximized. Hard soldering and laser welding
are used for bonding and fixing the various components, including the diode laser
on a heat sink, a photodiode, which monitors the laser output through the back
facet, a thermistor that monitors the temperature, and various optical elements to the
submount to achieve high reliability for a high-performance laser product in a butterfly
package. The actual fiber is mounted inside a so-called fiber tube subassembly, which
is welded to the wall of the package, and the fiber is threaded in through a hole and
BASIC DIODE LASER ENGINEERING PRINCIPLES
93
Figure 1.40 (a) Coupling efficiency versus laser facet–fiber tip distance calculated for laser
light emitted under 11◦ × 26◦ far-field divergence angles into 24.5◦ wedge-lensed fibers with
mode field diameters of 5.9 μm (solid line), 4.7 μm (dashed line), and 3.6 μm (dot–dashed
line). (b) Coupling efficiency versus fiber mode field diameter calculated for laser emission
into 24.5◦ wedge-lensed fibers (solid line) and fibers with parabolically shaped lenses (dashed
line). Experimental points from various different runs for coupling laser light into wedge-lensed
fibers.
attached to the submount or optical bench in front of the laser chip. Regarding loss of
coupling due to misalignment, it is important to consider both mode amplitude and
phase mismatching.
However, there is a conflict because systems that are more tolerant of amplitude
mismatches are less tolerant of phase mismatches and vice versa. This can be illustrated by a simple example: butt coupling between two fibers. For the same linear
displacement, there will be a smaller mismatch of the amplitudes with a larger mode
field diameter (MFD). In contrast, for the same phase error, the smaller MFD allows
a larger angular error. To achieve >90% coupling efficiency in a lensed fiber system, the lateral alignment accuracy is required to be better than 50 μm, something
that takes very careful process optimization to maintain while fixing the fiber by
laser welding. The coupling efficiency drops from its maximum value toward larger
facet–fiber distances with a typical rate of ∼
= 5% per micrometer (see Figure 1.40a).
Figures 1.40 and 1.41 show the dependence of the coupling efficiency on (i) the
free-space distance between the laser facet and fiber tip, (ii) the fiber MFD, (iii) the FF
angle of the laser in transverse lateral direction θ , and (iv) the FF angle in transverse
vertical direction θ ⊥ (Epperlein et al., 2000).
Key results are as follows:
r Calculated coupling efficiencies >90% at a facet–fiber gap of ∼
= 4 μm for a
laser with FF angles 11◦ × 26◦ and a 24.5◦ AR-coated wedge-lensed fiber with
MFD = 3.6 μm.
r Calculated coupling efficiencies >90% at MFD ∼
= 3.5 μm for a 24.5◦ wedgelensed fiber and for a laser with FF angles 10◦ × 25◦ with experimental coupling
values lower by 10%.
94
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
Figure 1.41 (a) Coupling efficiency versus laser transverse lateral divergence angle calculated for laser light emitted at transverse vertical angles of 21◦ (solid line), 19◦ (long
dashed line), 30◦ (dot–dashed line), and 15◦ (short-dashed line) into a 24.5◦ wedge-lensed
single-mode fiber with a mode field diameter of 5.9 μm. (b) Peak coupling efficiency versus
laser transverse vertical divergence angle calculated for laser light emitted at a transverse
lateral angle of 7◦ into a 24.5◦ wedge-lensed single-mode fiber with a mode field diameter of
5.9 μm.
r Calculated coupling efficiencies >85% at θ ∼
= 7◦ for a transverse vertical
FF angle θ ⊥ = 21◦ and a 24.5◦ wedge-lensed single-mode fiber with MFD =
5.9 μm.
In the preceding subsections, we discussed optical coupling for single-mode diode
lasers with diffraction-limited beams in both transverse directions. However, broadarea lasers typically 100 μm wide and 1 cm laser bars have a relatively poor beam
quality, which is usually expressed by the beam parameter product (BPP), defined
as half the beam waist diameter in focus times half the FF divergence angle. The
output beam of these lasers is characterized by a highly asymmetric profile with
regard to beam dimension and divergence angle. In the case of a laser bar, typical
values for the source width are 10 mm in the slow-axis direction and 1 μm in the
fast-axis direction with typical beam divergence angles of 5◦ and 35◦ , respectively.
This means that the resulting BPPs are highly asymmetric: in the slow direction
BPP ∼
=400 mm × mrad, which is far beyond the diffraction limit; and in the fast
direction BPP ∼
=1 mm × mrad, which is nearly diffraction limited (Köhler et al.,
2010). Efficient fiber coupling of such a diode laser is only possible if the different
BPPs are adapted by shifting beam quality from one direction to the other and
special symmetrization optics are applied for reshaping the beam (Bachmann et al.,
2007). This symmetrization of the BPPs is equivalent to a minimization of the overall
beam parameter product BPPtotal = (BPP2slow + BPP2fast )1/2 . The smallest possible
BPP is achieved with a diffraction-limited Gaussian beam and is proportional to
BASIC DIODE LASER ENGINEERING PRINCIPLES
95
the wavelength, and consequently fiber coupling becomes more difficult at longer
wavelengths.
1.4.3.4
Device operating temperature control
The strong temperature sensitivity of the diode laser characteristics including threshold current, output power, and lasing wavelength, but also of the laser long-term
reliability and lifetime, requires operating the laser under temperature-controlled
conditions. The stabilization of the operating laser temperature is usually realized
by mounting the laser platform, including a temperature sensor, on a thermo-electric
cooler (TEC) (Peltier). The sensor is typically a thermistor (thermally sensitive resistor; it has a large negative temperature coefficient for electrical resistance and
is formed from a sintered alloy of oxides or carbonates of Fe, Ni, Mn, Mo, and
Cu), which monitors the temperature and controls the cooling power of the TEC
to achieve constant operating temperature. This is standard practice for diode lasers
used as optical pumping sources for fiber amplifiers and as transmitters for coherent
communication systems. However, for high-power broad-area lasers and laser arrays
water coolers have to be used, because of the large heat load these devices generate.
For smaller heat loads, passive cooling is applied where the laser chip or bar on a
heat sink is hard-soldered onto an expansion-matched substrate such as CuW, which
is then clamped on a Cu heat exchanger. In the case of high heat loads, the device
on an expansion-matched submount is hard-soldered onto an expansion-matched
microchannel heat exchanger.
1.4.3.5
Hermetic sealing
Modules for high-performance diode lasers such as pump lasers and fiber optic
communication lasers are sealed hermetically to provide long-term stability and
reliability.
To realize hermetically sealed packages the electrical and optical input and output
terminals or ports have to be sealed hermetically:
r Electrical pins of TO headers are isolated from the package frame and sealed
with glass by melting glass powder packed between the pin and frame with a
subsequent oxidization to strengthen the seal.
r AR-coated optical windows partially metallized along the edge are joined to
the cap of TO cans by brazing with silver solder.
r Electrical terminals of rectangular-type packages, such as butterfly and miniDIL, are hard-soldered onto a metallized layer in the ceramic frame.
r Fibers are inserted into a ferrule and fixed with acrylate/epoxy or metallized
fibers are hard-soldered to the ferrule/frame.
The active components are wire-bonded each to a pin, the package is carefully
cleaned of organic contamination, and a desiccant is included inside the package to
getter moisture and organics. Before closing the package, an oxygen-rich atmosphere
96
SEMICONDUCTOR LASER ENGINEERING, RELIABILITY AND DIAGNOSTICS
is established inside it. This suppresses so-called package-induced failures (PIFs),
which are caused by a photothermal decomposition process of hydrocarbon traces in
the atmosphere on a surface exposed to high optical intensity. The chemical reaction
between hydrocarbons and oxygen burns off the hydrocarbons but leaves water as a
by-product, which can be gettered by the desiccant. The coverlid is put on by hard
soldering if the frame is metallized ceramic or by laser welding if the package frame
is metallic.
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